# zbMATH — the first resource for mathematics

## Mathematical Modelling of Natural Phenomena

 Short Title: Math. Model. Nat. Phenom. Publisher: EDP Sciences, Les Ulis ISSN: 0973-5348; 1760-6101/e Online: http://www.mmnp-journal.org/component/issues/?task=all&Itemid=121 Comments: Indexed cover-to-cover; Published electronic only as of Vol. 11 (2016). Print-ISSN until then: 0973-5348.
 Documents Indexed: 891 Publications (since 2006) References Indexed: 479 Publications with 17,518 References.
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#### Authors

 38 Volpert, Vitaly A. 14 Ibragimov, Ranis N. 10 Morozov, Andrew Yu. 9 Venturino, Ezio 8 Banerjee, Malay 8 Gorban, Alexander N. 8 Petrovskii, Sergei V. 8 Sequeira, Adélia 7 Kooi, Bob W. 7 Stéphanou, Angélique 6 Auger, Pierre M. 6 Ducrot, Arnaud 6 Ibragimov, Nail Hairullovich 6 Tyukin, Ivan Yu. 6 Zemzemi, Nejib 5 Adimy, Mostafa 5 Apreutesei, Narcisa C. 5 Băleanu, Dumitru I. 5 Bocharov, Gennady A. 5 Chaplain, Mark A. J. 5 Clairambault, Jean 5 Crauste, Fabien 5 Nec, Yana 5 Nepomnyashchy, Alexander A. 5 Ramm, Alexander G. 5 Vougalter, Vitali 5 Webb, Glenn Francis 4 Aboulaich, Rajae 4 Allali, Karam 4 Aniţa, Sebastian 4 Atangana, Abdon 4 Banks, Harvey Thomas 4 Boujena, Soumaya 4 Bravo de la Parra, Rafael 4 Génieys, Stéphane 4 Henry, Jacques 4 Kerbal, Sebti 4 Marvá, Marcos 4 Panteleev, Mikhail A. 4 Perthame, Benoît 4 Preziosi, Luigi 4 Pujo-Menjouet, Laurent 4 Ruzhansky, Michael V. 4 Sivashinsky, Gregory I. 4 Tosenberger, Alen 4 Volpert, Vladimir A. 4 Wong, Man Wah 4 Yousfi, Noura 3 Aguiar, Maíra 3 Agur, Zvia 3 Ahmed, Najma 3 Angstmann, Christopher N. 3 Area, Iván 3 Ataullakhanov, Fazoil I. 3 Augeraud-Véron, Emmanuelle 3 Boucekkine, Raouf 3 Bouchnita, Anass 3 Bowong, Samuel 3 Chechkin, Aleksei V. 3 Chekroun, Abdennasser 3 Cournède, Paul-Henry 3 Crooke, Philip S. III 3 Davidson, Fordyce A. 3 El Guarmah, El Mahdi 3 El-Khatib, Nader 3 Farkas, József Zoltán 3 Goldobin, Denis S. 3 Gómez-Aguilar, José Francisco 3 Hattaf, Khalid 3 Henry, Bruce I. 3 Jungck, John R. 3 Kafi, Oualid 3 Kagan, L. 3 Kaźmierczak, Bogdan 3 Kelbert, Mark Ya. 3 Kim, Nam-Il 3 Kiss, István Z. 3 Kogan, Yuri 3 Kosztołowicz, Tadeusz 3 Kumar, Devendra 3 Labate, Demetrio 3 Letort, V. 3 Lewandowska, Katarzyna D. 3 Lorenzi, Tommaso 3 Makarov, Valeri A. 3 Malchow, Horst 3 Marciniak-Czochra, Anna K. 3 Milner, Fabio Augusto 3 Molahajloo, Shahla 3 Novozhilov, Artem S. 3 Ovsyannikov, Ivan I. 3 Pousin, J. 3 Ruan, Shigui 3 Sakhnovich, Alexander L. 3 Scianna, Marco 3 Singh, Jagdev 3 Stepanyants, Yury A. 3 Stollenwerk, Nico 3 Suragan, Durvudkhan 3 Sveshnikova, Anastasia N. ...and 1,546 more Authors
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#### Fields

 491 Biology and other natural sciences (92-XX) 347 Partial differential equations (35-XX) 172 Ordinary differential equations (34-XX) 125 Fluid mechanics (76-XX) 98 Numerical analysis (65-XX) 89 Dynamical systems and ergodic theory (37-XX) 63 Systems theory; control (93-XX) 61 Probability theory and stochastic processes (60-XX) 53 Operator theory (47-XX) 47 Calculus of variations and optimal control; optimization (49-XX) 43 Statistical mechanics, structure of matter (82-XX) 40 Mechanics of deformable solids (74-XX) 39 Classical thermodynamics, heat transfer (80-XX) 36 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 21 Statistics (62-XX) 20 Real functions (26-XX) 16 General and overarching topics; collections (00-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 16 Computer science (68-XX) 14 Integral equations (45-XX) 13 Combinatorics (05-XX) 13 Quantum theory (81-XX) 13 Geophysics (86-XX) 13 Mathematics education (97-XX) 11 Special functions (33-XX) 11 Mechanics of particles and systems (70-XX) 11 Optics, electromagnetic theory (78-XX) 10 Difference and functional equations (39-XX) 9 Operations research, mathematical programming (90-XX) 6 Integral transforms, operational calculus (44-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Potential theory (31-XX) 5 Functional analysis (46-XX) 4 Measure and integration (28-XX) 4 Convex and discrete geometry (52-XX) 3 History and biography (01-XX) 3 Functions of a complex variable (30-XX) 3 Information and communication theory, circuits (94-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Sequences, series, summability (40-XX) 2 Abstract harmonic analysis (43-XX) 1 Number theory (11-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX)

#### Citations contained in zbMATH Open

529 Publications have been cited 3,003 times in 2,482 Documents Cited by Year
Pattern and waves for a model in population dynamics with nonlocal consumption of resources. Zbl 1201.92055
Genieys, S.; Volpert, V.; Auger, P.
2006
On nonlinear dynamics of predator-prey models with discrete delay. Zbl 1172.34046
Ruan, S.
2009
Unbounded Laplacians on graphs: basic spectral properties and the heat equation. Zbl 1207.47032
Keller, M.; Lenz, D.
2010
Inverse stable subordinators. Zbl 1274.60153
Meerschaert, M. M.; Straka, P.
2013
Regularity and blow up for active scalars. Zbl 1194.35490
Kiselev, A.
2010
Viscous shock capturing in a time-explicit discontinuous Galerkin method. Zbl 1220.65165
Klöckner, A.; Warburton, T.; Hesthaven, J. S.
2011
Epidemiological models and Lyapunov functions. Zbl 1337.92206
Fall, A.; Iggidr, A.; Sallet, G.; Tewa, J. J.
2007
Concentration in the nonlocal Fisher equation: the Hamilton-Jacobi limit. Zbl 1337.35077
Perthame, Benoît; Génieys, Stephane
2007
The construction of smooth Parseval frames of shearlets. Zbl 1266.42076
Guo, K.; Labate, D.
2013
A high-order unifying discontinuous formulation for the Navier-Stokes equations on 3D mixed grids. Zbl 1239.76044
Haga, T.; Gao, H.; Wang, Z. J.
2011
Dynamics of biomembranes: effect of the bulk fluid. Zbl 1231.92014
Bonito, A.; Nochetto, R. H.; Pauletti, M. S.
2011
Mathematical modeling of leukemogenesis and cancer stem cell dynamics. Zbl 1241.92045
Stiehl, T.; Marciniak-Czochra, A.
2012
Numerical computation of a fractional derivative with non-local and non-singular kernel. Zbl 1416.65190
Djida, Jean Daniel; Atangana, A.; Area, I.
2017
Wave-like solutions for nonlocal reaction-diffusion equations: a toy model. Zbl 1280.34066
Nadin, G.; Rossi, L.; Ryzhik, L.; Perthame, B.
2013
Facilitating the adoption of unstructured high-order methods amongst a wider community of fluid dynamicists. Zbl 1387.76002
Vincent, P. E.; Jameson, A.
2011
New numerical approach for fractional differential equations. Zbl 1406.65045
2018
A survey of methods for deciding whether a reaction network is multistationary. Zbl 1371.92148
Joshi, B.; Shiu, A.
2015
Selection theorem for systems with inheritance. Zbl 1337.92150
Gorban, A. N.
2007
Multiphase and multiscale trends in cancer modelling. Zbl 1166.92030
Preziosi, L.; Tosin, A.
2009
Global bifurcation for the Whitham equation. Zbl 1283.35108
Ehrnström, M.; Kalisch, H.
2013
Analysis of a population model structured by the cells molecular content. Zbl 1337.92174
Doumic, M.
2007
Competition of species with intra-specific competition. Zbl 1337.35068
Apreutesei, N.; Ducrot, A.; Volpert, V.
2008
On spectral stability of solitary waves of nonlinear Dirac equation in 1D. Zbl 1247.35117
Berkolaiko, G.; Comech, A.
2012
Ecoepidemiology: a more comprehensive view of population interactions. Zbl 1384.92060
Venturino, Ezio
2016
Nonharmonic analysis of boundary value problems without WZ condition. Zbl 1385.58013
Ruzhansky, M.; Tokmagambetov, N.
2017
Epidemic spread in networks: existing methods and current challenges. Zbl 1322.92076
Miller, J. C.; Kiss, I. Z.
2014
Continuous time random walks with reactions forcing and trapping. Zbl 1320.60135
Angstmann, C. N.; Donnelly, I. C.; Henry, B. I.
2013
Atherosclerosis initiation modeled as an inflammatory process. Zbl 1337.92108
El Khatib, N.; Génieys, S.; Volpert, V.
2007
Inside dynamics of delayed traveling waves. Zbl 1278.35044
Bonnefon, O.; Garnier, J.; Hamel, F.; Roques, L.
2013
Spatiotemporal dynamics in a spatial plankton system. Zbl 1197.92049
Upadhyay, R. K.; Wang, W.; Thakur, N. K.
2010
Spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in periodic habitats. Zbl 1358.92079
Kong, L.; Rawal, N.; Shen, W.
2015
The intersection of theory and application in elucidating pattern formation in developmental biology. Zbl 1181.35297
Othmer, H. G.; Painter, K.; Umulis, D.; Xue, C.
2009
Homogenization of a periodic parabolic Cauchy problem in the Sobolev space. Zbl 1203.35026
Suslina, T.
2010
Volume filling effect in modelling chemotaxis. Zbl 1184.35166
Wrzosek, D.
2010
Bifurcation thresholds in an SIR model with information-dependent vaccination. Zbl 1337.92223
d’Onofrio, A.; Manfredi, P.; Salinelli, E.
2007
Generalization of the Kermack-McKendrick SIR model to a patchy environment for a disease with latency. Zbl 1170.34056
Li, Jing; Zou, X.
2009
Properties of discrete framelet transforms. Zbl 1268.42073
Han, Bin
2013
Mathematics of Darwin’s diagram. Zbl 1321.92060
Bessonov, N.; Reinberg, N.; Volpert, V.
2014
On the use of the Hill functions in mathematical models of gene regulatory networks. Zbl 1337.92082
Santillán, M.
2008
Epidemiology of dengue fever: A model with temporary cross-immunity and possible secondary infection shows bifurcations and chaotic behaviour in wide parameter regions. Zbl 1337.92126
Aguiar, Maíra; Kooi, Bob; Stollenwerk, Nico
2008
Entire solutions in lattice delayed differential equations with nonlocal interaction: bistable cases. Zbl 1390.34219
Wang, Z.-C.; Li, W.-T.; Ruan, S.
2013
Patterns of zooplankton functional response in communities with vertical heterogeneity: a model study. Zbl 1337.92189
Morozov, A.; Arashkevich, E.
2008
Global asymptotic stability of equilibria in models for virus dynamics. Zbl 1337.92216
Prüss, J.; Zacher, R.; Schnaubelt, R.
2008
New aspects of fractional Biswas-Milovic model with Mittag-Leffler law. Zbl 1423.35415
Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru
2019
Approximating the stability region for a differential equation with a distributed delay. Zbl 1187.34097
Campbell, S. A.; Jessop, R.
2009
Methods of blood flow modelling. Zbl 1384.92024
Bessonov, N.; Sequeira, A.; Simakov, S.; Vassilevskii, Yu.; Volpert, V.
2016
Enrichment paradox induced by spatial heterogeneity in a phytoplankton - zooplankton system. Zbl 1337.92192
Poggiale, J.-C.; Gauduchon, M.; Auger, P.
2008
Wave of chaos and pattern formation in spatial predator-prey systems with Holling type IV predator response. Zbl 1337.35080
Upadhyay, R. K.; Kumari, N.; Rai, V.
2008
Semigroup analysis of structured parasite populations. Zbl 1187.92079
Farkas, J. Z.; Green, D. M.; Hinow, P.
2010
Examples of Lorenz-like attractors in Hénon-like maps. Zbl 1331.37040
Gonchenko, S. V.; Gonchenko, A. S.; Ovsyannikov, I. I.; Turaev, D. V.
2013
Quasichemical models of multicomponent nonlinear diffusion. Zbl 1234.35131
Gorban, A. N.; Sargsyan, H. P.; Wahab, H. A.
2011
On chemotaxis models with cell population interactions. Zbl 1197.35140
Wang, Z. A.
2010
An explicitly solvable nonlocal eigenvalue problem and the stability of a spike for a sub-diffusive reaction-diffusion system. Zbl 1275.35020
Nec, Y.; Ward, M. J.
2013
The importance of spatial distribution of stemness and proliferation state in determining tumor radioresponse. Zbl 1165.92022
Enderling, H.; Park, D.; Hlatky, L.; Hahnfeldt, P.
2009
Blood cell dynamics: half of a century of modelling. Zbl 1384.92027
Pujo-Menjouet, L.
2016
Rare mutations limit of a steady state dispersal evolution model. Zbl 1387.35027
Perthame, Benoit; Souganidis, P. E.
2016
A measure-theoretic model for collective cell migration and aggregation. Zbl 1314.35194
Colombi, A.; Scianna, M.; Preziosi, L.
2015
Optimal proliferation rate in a cell division model. Zbl 1337.92048
Michel, P.
2006
Dynamics of tuberculosis: the effect of direct observation therapy strategy (DOTS) in Nigeria. Zbl 1337.92212
Okuonghae, D.; Korobeinikov, A.
2007
The basic reproduction number of an infectious disease in a stable population: the impact of population growth rate on the eradication threshold. Zbl 1337.92208
Inaba, H.; Nishiura, H.
2008
Dynamical behavior of a stochastic SIRS epidemic model. Zbl 1337.34046
Hieu, N. T.; Du, N. H.; Auger, P.; Dang, N. H.
2015
Asymptotic behavior of solutions to diffusion problems with Robin and free boundary conditions. Zbl 1282.35071
Liu, Xiaowei; Lou, Bendong
2013
Memory effects in population dynamics : spread of infectious disease as a case study. Zbl 1316.92088
Pimenov, A.; Kelly, T. C.; Korobeinikov, A.; O’Callaghan, M. J. A.; Pokrovskii, A. V.; Rachinskii, D.
2012
Patterns and transitions to instability in an intraspecific competition model with nonlocal diffusion and interaction. Zbl 1336.92065
Aydogmus, O.
2015
A new fractional calculus model for the two-dimensional anomalous diffusion and its analysis. Zbl 1393.35280
Luchko, Yu.
2016
Application of Atangana-Baleanu fractional derivative to convection flow of MHD Maxwell fluid in a porous medium over a vertical plate. Zbl 1405.76065
Abro, K. A.; Khan, I.; Tassaddiq, A.
2018
Optimal control in coupled within-host and between-host models. Zbl 1294.49013
Numfor, E.; Bhattacharya, S.; Lenhart, S.; Martcheva, M.
2014
Numerical modelling of cell distribution in blood flow. Zbl 1333.92021
Bessonov, N.; Babushkina, E.; Golovashchenko, S. F.; Tosenberger, A.; Ataullakhanov, F.; Panteleev, M.; Tokarev, A.; Volpert, V.
2014
Asymptotic behavior of a discrete maturity structured system of hematopoietic stem cell dynamics with several delays. Zbl 1337.34074
Adimy, M.; Crauste, F.; El Abdllaoui, A.
2006
ATP production and necrosis formation in a tumour spheroid model. Zbl 1337.92099
Bertuzzi, A.; Fasano, A.; Gandolfi, A.; Sinisgalli, C.
2007
Reaction-difusion model of early carcinogenesis: the effects of influx of mutated cells. Zbl 1337.92047
Marciniak-Czochra, Anna; Kimmel, Marek
2008
Characterizations of two different fractional operators without singular kernel. Zbl 1423.26015
Yavuz, Mehmet
2019
On threshold eigenvalues and resonances for the linearized NLS equation. Zbl 1193.35212
Vougalter, V.
2010
Delay model of hematopoietic stem cell dynamics: Asymptotic stability and stability switch. Zbl 1186.34117
Crauste, F.
2009
On the form of smooth-front travelling waves in a reaction-diffusion equation with degenerate nonlinear diffusion. Zbl 1202.35050
Sherratt, J. A.
2010
Phytoplankton dynamics: from the behaviour of cells to a transport equation. Zbl 1201.92062
2006
Necessary optimality conditions for a Lotka-Volterra three species system. Zbl 1201.92058
Apreutesei, N. C.
2006
Free boundary problems associated with multiscale tumor models. Zbl 1172.35080
Friedman, A.
2009
Comparison of Perron and Floquet eigenvalues in age structured cell division cycle models. Zbl 1177.35052
Clairambault, J.; Gaubert, S.; Lepoutre, Th.
2009
Allee effect in Gause type predator-prey models: existence of multiple attractors, limit cycles and separatrix curves. A brief review. Zbl 1285.92024
González-Olivares, E.; Rojas-Palma, A.
2013
Patterns for competing populations with species specific nonlocal coupling. Zbl 1338.35237
Bayliss, A.; Volpert, V. A.
2015
Schrödinger operators on a half-line with inverse square potentials. Zbl 1320.47047
Kovařík, H.; Truc, F.
2014
Operational methods and new identities for Hermite polynomials. Zbl 1384.42017
Cesarano, C.
2017
Numerical approach to fractional blow-up equations with Atangana-Baleanu derivative in Riemann-Liouville sense. Zbl 1410.65323
2018
A different approach to the European option pricing model with new fractional operator. Zbl 1405.91658
Yavuz, M.; Özdemir, N.
2018
Typical atherosclerotic plaque morphology. Zbl 1337.92116
Poston, R. N.; Poston, D. R. M.
2007
Modelling of cancer growth, evolution and invasion: bridging scales and models. Zbl 1337.92020
Anderson, A. R. A.; Rejniak, K. A.; Gerlee, P.; Quaranta, V.
2007
The speed of epidemic waves in a one-dimensional lattice of SIR models. Zbl 1337.92217
Sazonov, Igor; Kelbert, Mark; Gravenor, Michael B.
2008
Spread pattern formation of H5N1-avian influenza and its implications for control strategies. Zbl 1337.92209
Liu, R.; Duvvuri, V. R. S. K.; Wu, J.
2008
Modeling and analysis of fractional neutral disturbance waves in arterial vessels. Zbl 1447.35336
Song, Feixue; Yu, Zheyuan; Yang, Hongwei
2019
Response functions in linear viscoelastic constitutive equations and related fractional operators. Zbl 1462.35294
Hristov, Jordan
2019
Double operator integrals and submajorization. Zbl 1214.46042
Potapov, D.; Sukochev, F.
2010
Generalized elastic model: fractional Langevin description, fluctuation relation and linear response. Zbl 1267.82103
Taloni, A.; Chechkin, A.; Klafter, J.
2013
Travelling waves in near-degenerate bistable competition models. Zbl 1202.35019
Alzahrani, E. O.; Davidson, F. A.; Dodds, N.
2010
Investigation of the migration/proliferation dichotomy and its impact on avascular glioma invasion. Zbl 1241.92036
Böttger, K.; Hatzikirou, H.; Chauviere, A.; Deutsch, A.
2012
The projection method for multidimensional framelet and wavelet analysis. Zbl 1303.42018
Han, B.
2014
On the discrete spectrum of Robin Laplacians in conical domains. Zbl 1390.35208
Pankrashkin, Konstantin
2016
An ecoepidemic model with prey herd behavior and predator feeding saturation response on both healthy and diseased prey. Zbl 1384.37112
Banerjee, M.; Kooi, Bob W.; Venturino, E.
2017
Human immunodeficiency virus infection: from biological observations to mechanistic mathematical modelling. Zbl 1261.92033
Bocharov, G.; Chereshnev, V.; Gainova, I.; Bazhan, S.; Bachmetyev, B.; Argilaguet, J.; Martinez, J.; Meyerhans, A.
2012
Modeling morphogenesis in silico and in vitro: towards quantitative, predictive, cell-based modeling. Zbl 1167.92004
Merks, R. M. H.; Koolwijk, P.
2009
On numerical approximation of atangana-baleanu-Caputo fractional integro-differential equations under uncertainty in Hilbert space. Zbl 07372369
Al-Smadi, Mohammed; Dutta, Hemen; Hasan, Shatha; Momani, Shaher
2021
On the maximization problem for solutions of reaction-diffusion equations with respect to their initial data. Zbl 07372601
Nadin, Grégoire; Toledo Marrero, Ana Isis
2020
Discrete and continuum phenotype-structured models for the evolution of cancer cell populations under chemotherapy. Zbl 1467.92101
Stace, Rebecca E. A.; Stiehl, Thomas; Chaplain, Mark A. J.; Marciniak-Czochra, Anna; Lorenzi, Tommaso
2020
A three phase model to investigate the effects of dead material on the growth of avascular tumours. Zbl 1467.92061
Lewin, Thomas D.; Maini, Philip K.; Moros, Eduardo G.; Enderling, Heiko; Byrne, Helen M.
2020
New aspects of fractional Biswas-Milovic model with Mittag-Leffler law. Zbl 1423.35415
Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru
2019
Characterizations of two different fractional operators without singular kernel. Zbl 1423.26015
Yavuz, Mehmet
2019
Modeling and analysis of fractional neutral disturbance waves in arterial vessels. Zbl 1447.35336
Song, Feixue; Yu, Zheyuan; Yang, Hongwei
2019
Response functions in linear viscoelastic constitutive equations and related fractional operators. Zbl 1462.35294
Hristov, Jordan
2019
Fractional order model of immune cells influenced by cancer cells. Zbl 1418.34033
Ucar, Esmehan; Özdemir, Necati; Altun, Eren
2019
Modeling the dynamics of hepatitis E. Zbl 1420.92106
Khan, Muhammad Altaf; Hammouch, Zakia; Baleanu, Dumitru
2019
Immune response in HIV epidemics for distinct transmission rates and for saturated CTL response. Zbl 1421.35375
Carvalho, Ana R. M.; Pinto, Carla M. A.
2019
A hybrid analytical algorithm for nonlinear fractional wave-like equations. Zbl 1423.65001
Kumar, Devendra; Singh, Jagdev; Purohit, Sunil Dutt; Swroop, Ram
2019
The existence and asymptotic stability of periodic solutions with an interior layer of Burgers type equations with modular advection. Zbl 1447.35030
Nefedov, Nikolay
2019
Canards existence in the Hindmarsh-Rose model. Zbl 1423.34074
Ginoux, Jean-Marc; Llibre, Jaume; Tchizawa, Kiyoyuki
2019
The optimal population size under pollution and migration externalities: a spatial control approach. Zbl 1457.91300
La Torre, Davide; Liuzzi, Danilo; Marsiglio, Simone
2019
A new approach to capture heterogeneity in groundwater problem: an illustration with an Earth equation. Zbl 07095088
Atangana, Abdon; Alqahtani, Rubayyi T.
2019
Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling. Zbl 1437.35244
Muravnik, Andrey B.
2019
An infection age-space-structured SIR epidemic model with Dirichlet boundary condition. Zbl 1429.35111
Chekroun, Abdennasser; Kuniya, Toshikazu
2019
Mathematical modelling of atherosclerosis. Zbl 1431.92031
El Khatib, N.; Kafi, O.; Sequeira, A.; Simakov, S.; Vassilevski, Yu.; Volpert, V.
2019
Geographic environmental Kuznets curves: the optimal growth linear-quadratic case. Zbl 1421.49029
Boucekkine, Raouf; Fabbri, Giorgio; Federico, Salvatore; Gozzi, Fausto
2019
Distributed optimal control models in environmental economics: a review. Zbl 1457.91282
Augeraud-Véron, Emmanuelle; Boucekkine, Raouf; Veliov, Vladimir M.
2019
A Nash game algorithm for the solution of coupled conductivity identification and data completion in cardiac electrophysiology. Zbl 1421.35077
Chamekh, Rabeb; Kallel, Moez; Zemzemi, Nejib
2019
Multiscale dynamics of an adaptive catalytic network. Zbl 1418.37086
Kuehn, Christian
2019
New numerical approach for fractional differential equations. Zbl 1406.65045
2018
Application of Atangana-Baleanu fractional derivative to convection flow of MHD Maxwell fluid in a porous medium over a vertical plate. Zbl 1405.76065
Abro, K. A.; Khan, I.; Tassaddiq, A.
2018
Numerical approach to fractional blow-up equations with Atangana-Baleanu derivative in Riemann-Liouville sense. Zbl 1410.65323
2018
A different approach to the European option pricing model with new fractional operator. Zbl 1405.91658
Yavuz, M.; Özdemir, N.
2018
Uniform asymptotic stability of a fractional tuberculosis model. Zbl 1407.92133
Wojtak, Weronika; Silva, Cristiana J.; Torres, Delfim F. M.
2018
Fractional compound Poisson processes with multiple internal states. Zbl 1405.35189
Xu, Pengbo; Deng, Weihua
2018
Exact solutions for the blood flow through a circular tube under the influence of a magnetic field using fractional Caputo-Fabrizio derivatives. Zbl 1408.37147
Riaz, M. B.; Zafar, A. A.
2018
A reliable mixed method for singular integro-differential equations of non-integer order. Zbl 1451.65232
Baleanu, Dumitru; Darzi, Rahmat; Agheli, Bahram
2018
Fourth-order fractional diffusion model of thermal grooving: integral approach to approximate closed form solution of the Mullins model. Zbl 1405.26006
Hristov, Jordan
2018
Numerical and analytical solutions of nonlinear differential equations involving fractional operators with power and Mittag-Leffler kernel. Zbl 1462.34022
Yépez-Martínez, H.; Gómez-Aguilar, J. F.
2018
Existence and regularity of mild solutions to fractional stochastic evolution equations. Zbl 1405.60102
Zou, G. A.; Wang, B.
2018
Preface: Modelling in ecology, epidemiology and evolution. Zbl 1405.00025
Morozov, A.
2018
Adaptive fitness landscape for replicator systems: to maximize or not to maximize. Zbl 1405.92161
Bratus, Alexander S.; Semenov, Yuri S.; Novozhilov, Artem S.
2018
Stabilizing effect of intra-specific competition on prey-predator dynamics with intraguild predation. Zbl 1406.34075
Namba, Toshiyuki; Takeuchi, Yasuhiro; Banerjee, Malay
2018
Steady state analysis of a syntrophic model: the effect of a new input substrate concentration. Zbl 1407.34063
Daoud, Y.; Abdellatif, N.; Sari, T.; Harmand, J.
2018
Net reproduction functions for nonlinear structured population models. Zbl 1457.92135
Farkas, József Z.
2018
Mathematical study of a single leukocyte in microchannel flow. Zbl 1405.35222
Boujena, S.; Kafi, O.; Sequeira, A.
2018
Catching platelets from the bloodflow: the role of the conformation of von Willebrand factor. Zbl 1405.76071
Belyaev, Aleksey V.
2018
Applications of fractional derivatives to nanofluids: exact and numerical solutions. Zbl 1405.76062
Aman, Sidra; Khan, Ilyas; Ismail, Zulkhibri; Salleh, Mohd Zuki
2018
First integral method for non-linear differential equations with conformable derivative. Zbl 1458.35463
Yépez-Martínez, H.; Gómez-Aguilar, J. F.; Atangana, Abdon
2018
Prey herd behavior modeled by a generic non-differentiable functional response. Zbl 1405.92241
Vilches, Karina; González-Olivares, Eduardo; Rojas-Palma, Alejandro
2018
An economic-demographic dynamical system. Zbl 1405.35220
Zincenko, A.; Petrovskii, S.; Volpert, V.
2018
Interactions between leaf-cutter ants and fungus garden: effects of division of labor, age polyethism, and egg cannibalism. Zbl 1408.37148
Rodriguez Rodriguez, Marisabel; Smith, Nathan; Phan, Tin; Woodbury, Jonathan; Kang, Yun
2018
Characterizations of nuclear pseudo-differential operators on $$\mathbb{Z}$$ with some applications. Zbl 07007759
Jamalpourbirgani, Majid
2018
Reconstruction of the Robin boundary condition and order of derivative in time fractional heat conduction equation. Zbl 1405.35180
Brociek, Rafał; Słota, Damian
2018
Singular perturbed components of flows – linear precursors of shock waves. Zbl 1405.76037
Chashechkin, Yuli D.
2018
Invariant solutions and shock atmospheric waves in a thin circular layer. Zbl 1408.35194
Ibragimov, Nail H.; Ibragimov, Ranis N.; Kovalev, Vladimir F.
2018
Calibration of reduced-order model for a coupled Burgers equations based on PC-EnKF. Zbl 1405.65130
Wang, Yuepeng; Cheng, Yue; Zhang, Zongyuan; Lin, Guang
2018
Normal form for transverse instability of the line soliton with a nearly critical speed of propagation. Zbl 1405.35187
Pelinovsky, Dmitry
2018
Numerical computation of a fractional derivative with non-local and non-singular kernel. Zbl 1416.65190
Djida, Jean Daniel; Atangana, A.; Area, I.
2017
Nonharmonic analysis of boundary value problems without WZ condition. Zbl 1385.58013
Ruzhansky, M.; Tokmagambetov, N.
2017
Operational methods and new identities for Hermite polynomials. Zbl 1384.42017
Cesarano, C.
2017
An ecoepidemic model with prey herd behavior and predator feeding saturation response on both healthy and diseased prey. Zbl 1384.37112
Banerjee, M.; Kooi, Bob W.; Venturino, E.
2017
On the half-plane Dirichlet problem for differential-difference elliptic equations with several nonlocal terms. Zbl 1390.35391
Muravnik, A.
2017
Elliptic functional differential equations with incommensurable contractions. Zbl 1386.35066
Rossovskii, L.
2017
Inverse problems of a fractional differential equation with Bessel operator. Zbl 1388.35220
Al-Musalhi, F.; Al-Salti, N.; Kerbal, S.
2017
Nonlocal problems in the mechanics of three-layer shells. Zbl 1386.35078
Onanov, G. G.; Skubachevskii, A. L.
2017
A seasonal model for West Nile virus. Zbl 1384.92058
Moschini, P.; Bisanzio, D.; Pugliese, A.
2017
Dynamics of a stochastic viral infection model with immune response. Zbl 1391.92023
Mahrouf, M.; Hattaf, K.; Yousfi, N.
2017
Delayed nonlocal reaction-diffusion model for hematopoietic stem cell dynamics with Dirichlet boundary conditions. Zbl 1387.35583
Adimy, M.; Chekroun, A.; Kuniya, T.
2017
A discrete predator-prey ecoepidemic model. Zbl 1385.92038
Bravo de la Parra, Rafael; Marvá, M.; Sánchez, E.; Sanz, L.
2017
Linear partial divided-difference equation satisfied by multivariate orthogonal polynomials on quadratic lattices. Zbl 1384.33023
Tcheutia, D. D.; Tefo, Y. Guemo; Foupouagnigni, M.; Godoy, E.; Area, I.
2017
Optimal spraying in biological control of pests. Zbl 1384.92063
Silva, C. J.; Torres, D. F. M.; Venturino, E.
2017
Stochastic sensitivity analysis of noise-induced mixed-mode oscillations in Morris-Lecar neuron model. Zbl 1384.37118
Slepukhina, E.
2017
Noise enhanced signaling in STDP driven spiking-neuron network. Zbl 1384.92018
Lobov, S. A.; Zhuravlev, M. O.; Makarov, V. A.; Kazantsev, V. B.
2017
On HIV model with adaptive immune response, two saturated rates and therapy. Zbl 1385.34034
Allali, K.; Tabit, Y.; Harroudi, S.
2017
Dynamics of hepatitis C virus infection: mathematical modeling and parameter estimation. Zbl 1385.34037
Rihan, F. A.; Sheek-Hussein, M.; Tridane, A.; Yafia, R.
2017
The neutral-fractional telegraph equation. Zbl 1398.35262
2017
Existence and stabilization of a Kirchhoff moving string with a distributed delay in the boundary feedback. Zbl 1387.35396
Kelleche, A.; Tatar, N.-E.
2017
Migration effects on population dynamics of the honeybee-mite interactions. Zbl 1384.37117
Messan, K.; Degrandi-Hoffman, G.; Castillo-Chavez, C.; Kang, Yun
2017
On the well-posedness of the magnetic Schrödinger-Poisson system in $$\mathbb R^3$$. Zbl 1390.82060
Barbaroux, J.-M.; Vougalter, Vitali
2017
Bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. Zbl 1384.37068
Gonchenko, M.; Gonchenko, S.; Ovsyannikov, I.
2017
Some comprehensive inequalities consisting of Mittag-Leffler type functions in the complex plane. Zbl 1385.30002
Irmak, H.; Agarwal, P.
2017
Solvability of a nonlocal boundary value problem involving fractional derivative operators. Zbl 1386.35071
Kerbal, S.; Kadirkulov, B. J.; Turmetov, B.
2017
On isoperimetric inequalities for the Cauchy-Robin heat operator. Zbl 1390.35193
Kassymov, A.; Sadybekov, M.; Suragan, D.
2017
On stability of the solution of multidimensional inverse problem for the Schrödinger equation. Zbl 1390.35411
Berdyshev, A. S.; Sultanov, Murat A.
2017
Two forms of gradient approximation for an optimization problem for the heat equation. Zbl 1412.49049
Serovajsky, S.; Shakenov, I.
2017
Limb movement in dynamic situations based on generalized cognitive maps. Zbl 1390.93582
Villacorta-Atienza, J. A.; Calvo, C.; Lobov, S.; Makarov, V. A.
2017
Analysis of an interneuron gamma mechanism for cross-frequency coupling. Zbl 1384.92029
Chehelcheraghi, Mojtaba; Nakatani, C.; van Leeuwen, C.
2017
Discretization of fractional differential equations by a piecewise constant approximation. Zbl 1416.65245
Angstmann, C. N.; Henry, B. I.; Jacobs, B. A.; Mcgann, A. V.
2017
Layer solutions for a one-dimensional nonlocal model of Ginzburg-Landau type. Zbl 1390.35393
Chen, K.-S.; Muratov, C. B.; Yan, X.
2017
Stabilization by delay distributed feedback control. Zbl 1381.93088
Domoshnitsky, A.; Volinsky, I.; Polonsky, A.; Sitkin, A.
2017
Patchy, not patchy, or how much patchy? Classification of spatial patterns appearing in a model of biological invasion. Zbl 1384.92052
Petrovskaya, N.; Zhang, W.
2017
Analysis of functional-differential equation with orthotropic contractions. Zbl 1386.35067
Tasevich, A.
2017
Impact of hygiene, famine and environment on transmission and spread of cholera. Zbl 1384.92055
Dangbé, E.; Békollé, D.; Irépran, Damakoa; Perasso, Antoine
2017
Dynamics of a two subpopulations system including immigration. Zbl 1390.35366
Zincenko, A.; Petrovskii, S.
2017
Approximate conservation laws for an integrable Boussinesq system. Zbl 1390.35252
Ali, A.; Juliussen, B.-S.; Kalisch, Henrik
2017
Boundary value problem for the time-fractional telegraph equation with Caputo derivatives. Zbl 1388.35213
Mamchuev, M. O.
2017
Non-local boundary problem with integral form transmitting condition for fractional mixed type equation in a composite domain. Zbl 1387.35607
Kerbal, S.; Karimov, E.; Rakhmatullaeva, N.
2017
Cauchy problem for system of the Burgers equations arising in the two-velocity hydrodynamics. Zbl 1407.35055
Vasiliev, G.; Imomnazarov, Kh.; Kalimoldayev, M.; Mamasoliyev, B.
2017
Mathematical modeling of equatorial atmospheric waves similar to those travelling along a hexagon-shaped path at the North Pole of Saturn. Zbl 1445.85002
Ibragimov, R. N.
2017
New mechanisms of disorder tissue model. Zbl 1417.92038
Petrov, V. S.; Kryukov, A. K.; Osipov, G. V.
2017
Decision making in an intracellular genetic classifier. Zbl 1384.92007
Abrego, L.; Zaikin, Alexey
2017
Chaos in neural oscillators induced by unidirectional electrical coupling. Zbl 1384.37114
García-Vellisca, M. A.; Jaimes-Reátegui, R.; Pisarchik, Alexander N.
2017
Delay-independent synchronization in ring networks of identical/non-identical systems with transmission delay couplings. Zbl 1386.34125
Yanagi, D.; Oguchi, T.; Suzuki, M.
2017
Modelling stochastic and deterministic behaviours in virus infection dynamics. Zbl 1382.35317
Sazonov, I.; Grebennikov, D.; Kelbert, M.; Bocharov, G.
2017
Reducing the latent CD4$$^+$$ cells reservoirs in HIV infection with optimal HAART therapy. Zbl 1382.35319
Tridane, A.; El Boukari, B.; Hattaf, K.; Yousfi, N.
2017
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#### Cited by 3,841 Authors

 67 Volpert, Vitaly A. 25 Venturino, Ezio 22 Banerjee, Malay 19 Morozov, Andrew Yu. 18 Băleanu, Dumitru I. 18 Vougalter, Vitali 17 Ruzhansky, Michael V. 15 Wang, Zhi Cheng 14 Labate, Demetrio 14 Tokmagambetov, Niyaz Esenzholovich 14 Webb, Glenn Francis 13 Chaplain, Mark A. J. 13 Li, Wan-Tong 13 Perthame, Benoît 13 Suslina, Tat’yana Aleksandrovna 13 Trofimchuk, Sergei I. 12 Bocharov, Gennady A. 12 Henry, Bruce I. 12 Keller, Matthias 12 Kumar Upadhyay, Ranjit 12 Marciniak-Czochra, Anna K. 12 Ruan, Shigui 11 Angstmann, Christopher N. 11 Preziosi, Luigi 10 Bao, Xiongxiong 10 Ducrot, Arnaud 10 Gómez-Aguilar, José Francisco 10 Guo, Kanghui 10 Mackey, Michael Charles 10 Ward, Michael J. 10 Wu, Shiliang 9 Aniţa, Sebastian 9 Bowong, Samuel 9 Byrne, Helen Mary 9 Gonchenko, Sergey V. 9 Han, Bin 9 Kalisch, Henrik 9 Kuniya, Toshikazu 9 Lorenzi, Tommaso 9 Owolabi, Kolade Matthew 9 Petrovskii, Sergei V. 9 Scianna, Marco 9 Wang, Weiming 8 Adimy, Mostafa 8 Apreutesei, Narcisa C. 8 Chekroun, Abdennasser 8 Deng, Weihua 8 Farkas, József Zoltán 8 Karev, Georgiĭ Petrovich 8 Kooi, Bob W. 8 Korobeinikov, Andrei 8 Leonenko, Nikolai N. 8 Magal, Pierre 8 Nane, Erkan 8 Pelinovsky, Dmitry Efimovich 8 Ptashnyk, Mariya 8 Samanta, Guru Prasad 8 Sandev, Trifce 8 Sequeira, Adélia 8 Stollenwerk, Nico 8 Thieme, Horst R. 8 Winkler, Michael 8 Zhuang, Xiaosheng 7 Aguiar, Maíra 7 Atangana, Abdon 7 Bayliss, Alvin 7 Clairambault, Jean 7 Cournède, Paul-Henry 7 Crauste, Fabien 7 Dai, Binxiang 7 Golénia, Sylvain 7 Henderson, Christopher 7 Jameson, Antony 7 Kühn, Christian 7 Lenz, Daniel H. 7 Okuonghae, Daniel 7 Rachinskii, Dmitrii I. 7 Schmidt, Marcel 7 Sene, Ndolane 7 Surulescu, Christina 7 Vincent, Peter E. 7 Volpert, Vladimir A. 6 Ascione, Giacomo 6 Bouchnita, Anass 6 Colombi, Annachiara 6 Comech, Andrew 6 Damanik, David 6 Doumic, Marie 6 Fasano, Antonio 6 Gatica, Gabriel N. 6 Génieys, Stéphane 6 Han, Bang-Sheng 6 Hattaf, Khalid 6 Jin, Zhen 6 Khan, Muhammad Altaf 6 Kiss, István Z. 6 Komarova, Natalia L. 6 Lewis, Mark Alun 6 Lowengrub, John Samuel 6 Maini, Philip Kumar ...and 3,741 more Authors
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#### Cited in 370 Journals

 123 Mathematical Modelling of Natural Phenomena 122 Journal of Theoretical Biology 101 Journal of Mathematical Biology 81 Bulletin of Mathematical Biology 59 Journal of Computational Physics 58 Journal of Mathematical Analysis and Applications 55 Mathematical Biosciences 50 Discrete and Continuous Dynamical Systems. Series B 49 Chaos, Solitons and Fractals 48 Journal of Differential Equations 43 Nonlinear Analysis. Real World Applications 41 Applied Mathematics and Computation 37 Mathematical Biosciences and Engineering 30 SIAM Journal on Applied Mathematics 27 Journal of Biological Dynamics 25 Journal of Functional Analysis 24 Journal of Scientific Computing 23 Applied Mathematical Modelling 23 Chaos 22 Computers & Mathematics with Applications 22 Computer Methods in Applied Mechanics and Engineering 22 Journal of Computational and Applied Mathematics 22 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 21 Computers and Fluids 20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 20 Discrete and Continuous Dynamical Systems 20 Communications in Nonlinear Science and Numerical Simulation 19 Discrete Dynamics in Nature and Society 19 International Journal of Biomathematics 18 Physica D 17 Mathematical Methods in the Applied Sciences 17 Abstract and Applied Analysis 17 SIAM Journal on Applied Dynamical Systems 17 Discrete and Continuous Dynamical Systems. Series S 16 Applicable Analysis 16 Journal of Mathematical Physics 16 Advances in Mathematics 15 Transactions of the American Mathematical Society 15 Applied Numerical Mathematics 15 Applied Mathematics Letters 15 Fractional Calculus & Applied Analysis 14 Journal of Fluid Mechanics 14 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 14 Journal of Dynamics and Differential Equations 14 Nonlinear Dynamics 14 Journal of Biological Systems 13 Nonlinearity 13 SIAM Journal on Mathematical Analysis 13 Complexity 13 The Journal of Fourier Analysis and Applications 12 Journal of Nonlinear Science 12 Advances in Difference Equations 11 Acta Applicandae Mathematicae 11 Applied and Computational Harmonic Analysis 11 St. Petersburg Mathematical Journal 11 Journal of Mathematical Chemistry 10 Integral Equations and Operator Theory 10 Computational and Applied Mathematics 10 Mathematical Problems in Engineering 10 Journal of Pseudo-Differential Operators and Applications 10 Journal of Mathematics 9 Physica A 9 Mathematical and Computer Modelling 9 Annales Henri Poincaré 9 Mathematics 8 Archive for Rational Mechanics and Analysis 8 Journal of Statistical Physics 8 Letters in Mathematical Physics 8 Proceedings of the American Mathematical Society 8 European Journal of Applied Mathematics 8 Stochastic Processes and their Applications 8 Russian Journal of Numerical Analysis and Mathematical Modelling 8 Communications on Pure and Applied Analysis 8 Journal of Applied Mathematics and Computing 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 Computational & Mathematical Methods in Medicine 7 Communications in Mathematical Physics 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Automatica 7 Mathematics and Computers in Simulation 7 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 7 International Journal of Computer Mathematics 7 Differential Equations and Dynamical Systems 7 Multiscale Modeling & Simulation 6 Mathematics of Computation 6 Functional Analysis and its Applications 6 NoDEA. Nonlinear Differential Equations and Applications 6 Advances in Computational Mathematics 6 Journal of Evolution Equations 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Networks and Heterogeneous Media 5 Journal of the Franklin Institute 5 Mathematical Notes 5 International Journal for Numerical Methods in Engineering 5 Journal of Optimization Theory and Applications 5 Ricerche di Matematica 5 SIAM Journal on Numerical Analysis 5 Theoretical Population Biology 5 Chinese Annals of Mathematics. Series B 5 Stochastic Analysis and Applications ...and 270 more Journals
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#### Cited in 58 Fields

 1,302 Biology and other natural sciences (92-XX) 1,054 Partial differential equations (35-XX) 485 Ordinary differential equations (34-XX) 325 Numerical analysis (65-XX) 238 Fluid mechanics (76-XX) 201 Dynamical systems and ergodic theory (37-XX) 176 Probability theory and stochastic processes (60-XX) 173 Operator theory (47-XX) 111 Calculus of variations and optimal control; optimization (49-XX) 87 Systems theory; control (93-XX) 86 Harmonic analysis on Euclidean spaces (42-XX) 82 Integral equations (45-XX) 79 Real functions (26-XX) 79 Statistical mechanics, structure of matter (82-XX) 74 Mechanics of deformable solids (74-XX) 62 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 58 Quantum theory (81-XX) 51 Combinatorics (05-XX) 36 Global analysis, analysis on manifolds (58-XX) 35 Difference and functional equations (39-XX) 34 Special functions (33-XX) 33 Functional analysis (46-XX) 31 Statistics (62-XX) 29 Classical thermodynamics, heat transfer (80-XX) 27 Information and communication theory, circuits (94-XX) 25 Operations research, mathematical programming (90-XX) 24 Computer science (68-XX) 20 Approximations and expansions (41-XX) 19 Integral transforms, operational calculus (44-XX) 18 Mechanics of particles and systems (70-XX) 15 Geophysics (86-XX) 12 Optics, electromagnetic theory (78-XX) 11 Measure and integration (28-XX) 10 Number theory (11-XX) 10 Convex and discrete geometry (52-XX) 8 Functions of a complex variable (30-XX) 8 Potential theory (31-XX) 7 General and overarching topics; collections (00-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Abstract harmonic analysis (43-XX) 5 Topological groups, Lie groups (22-XX) 4 History and biography (01-XX) 4 Differential geometry (53-XX) 3 Field theory and polynomials (12-XX) 2 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Commutative algebra (13-XX) 2 Algebraic geometry (14-XX) 2 Several complex variables and analytic spaces (32-XX) 2 General topology (54-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 $$K$$-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)