## Atangana, Abdon

Compute Distance To:
 Author ID: atangana.abdon Published as: Atangana, Abdon; Atangana, A.; Abdon, Atangana External Links: ORCID · Wikidata · Google Scholar · ResearchGate · dblp
 Documents Indexed: 170 Publications since 2013, including 4 Books 8 Contributions as Editor Co-Authors: 103 Co-Authors with 162 Joint Publications 3,331 Co-Co-Authors
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### Serials

 33 Chaos, Solitons and Fractals 18 Abstract and Applied Analysis 15 Discrete and Continuous Dynamical Systems. Series S 13 Advances in Difference Equations 12 Mathematical Problems in Engineering 8 Journal of Nonlinear Science and Applications 6 Mathematical Methods in the Applied Sciences 6 Journal of Computational and Applied Mathematics 5 Chaos 5 Mathematical Modelling of Natural Phenomena 4 Numerical Methods for Partial Differential Equations 4 Fractals 3 Mathematical Biosciences and Engineering 2 Applied Mathematics and Computation 2 Computational and Applied Mathematics 2 Journal of Vibration and Control 2 International Journal of Biomathematics 1 Journal of Computational Physics 1 Physica A 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics and Computers in Simulation 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Applied Mathematical Modelling 1 Filomat 1 Engineering Analysis with Boundary Elements 1 Communications in Nonlinear Science and Numerical Simulation 1 Fundamenta Informaticae 1 Discrete and Continuous Dynamical Systems. Series B 1 Entropy 1 Boundary Value Problems 1 Springer Series in Computational Mathematics 1 Communications in Theoretical Physics 1 Advances in Mathematical Physics 1 Advances in Applied Mathematics and Mechanics 1 Journal of Mathematical Analysis 1 Journal of Applied Analysis and Computation 1 Open Mathematics 1 Information Technology, Management and Operations Research Practices
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### Fields

 84 Partial differential equations (35-XX) 72 Numerical analysis (65-XX) 50 Ordinary differential equations (34-XX) 45 Real functions (26-XX) 26 Biology and other natural sciences (92-XX) 16 Fluid mechanics (76-XX) 11 Dynamical systems and ergodic theory (37-XX) 10 Integral transforms, operational calculus (44-XX) 10 Geophysics (86-XX) 9 General and overarching topics; collections (00-XX) 9 Operator theory (47-XX) 6 Measure and integration (28-XX) 5 Special functions (33-XX) 5 Mechanics of deformable solids (74-XX) 4 Difference and functional equations (39-XX) 4 Integral equations (45-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Computer science (68-XX) 3 Systems theory; control (93-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 General topology (54-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Number theory (11-XX) 1 Potential theory (31-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX)

### Citations contained in zbMATH Open

126 Publications have been cited 2,175 times in 1,220 Documents Cited by Year
Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order. Zbl 1360.34150
Atangana, Abdon; Koca, Ilknur
2016
On the new fractional derivative and application to nonlinear Fisher’s reaction-diffusion equation. Zbl 1410.35272
Atangana, Abdon
2016
A fractional epidemiological model for computer viruses pertaining to a new fractional derivative. Zbl 1426.68015
Singh, Jagdev; Kumar, Devendra; Hammouch, Zakia; Atangana, Abdon
2018
New properties of conformable derivative. Zbl 1354.26008
Atangana, Abdon; Baleanu, Dumitru; Alsaedi, Ahmed
2015
Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Zbl 1374.28002
Atangana, Abdon
2017
Analysis of the Keller-Segel model with a fractional derivative without singular kernel. Zbl 1338.35458
2015
Fractional derivatives with no-index law property: application to chaos and statistics. Zbl 1415.34010
Atangana, Abdon; Gómez-Aguilar, J. F.
2018
On the stability and convergence of the time-fractional variable order telegraph equation. Zbl 1349.65263
Atangana, Abdon
2015
A note on fractional order derivatives and table of fractional derivatives of some special functions. Zbl 1276.26010
Atangana, Abdon; Secer, Aydin
2013
New numerical approach for fractional differential equations. Zbl 1406.65045
2018
Numerical approximation of Riemann-Liouville definition of fractional derivative: from Riemann-Liouville to Atangana-Baleanu. Zbl 1417.65113
Atangana, Abdon; Gómez-aguilar, J. F.
2018
On the formulation of Adams-bashforth scheme with Atangana-Baleanu-Caputo fractional derivative to model chaotic problems. Zbl 1409.34016
2019
Solving a system of fractional partial differential equations arising in the model of HIV infection of $$\mathrm{CD4}^{+}$$ cells and attractor one-dimensional Keller-Segel equations. Zbl 1380.92026
Atangana, Abdon; Alabaraoye, Ernestine
2013
Analysis and application of new fractional Adams-Bashforth scheme with Caputo-Fabrizio derivative. Zbl 1380.65120
2017
Blind in a commutative world: simple illustrations with functions and chaotic attractors. Zbl 1415.34009
Atangana, Abdon
2018
Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws. Zbl 1374.34296
Atangana, Abdon; Gómez-Aguilar, J. F.
2017
The time-fractional coupled-Korteweg-de-Vries equations. Zbl 1291.35273
Atangana, Abdon; Secer, Aydin
2013
On the new fractional derivative and application to nonlinear Baggs and Freedman model. Zbl 1335.34079
Atangana, Abdon; Koca, Ilknur
2016
Numerical computation of a fractional derivative with non-local and non-singular kernel. Zbl 1416.65190
Djida, Jean Daniel; Atangana, A.; Area, I.
2017
Numerical approximation of nonlinear fractional parabolic differential equations with Caputo-Fabrizio derivative in Riemann-Liouville sense. Zbl 1422.65178
2017
New fractional derivatives with non-singular kernel applied to the Burgers equation. Zbl 1394.35565
Saad, Khaled M.; Atangana, Abdon; Baleanu, Dumitru
2018
Analysis of non-homogeneous heat model with new trend of derivative with fractional order. Zbl 1360.35080
2016
New fractional derivatives applied to the Korteweg-de Vries and Korteweg-de Vries-Burgers equations. (New fractional derivatives applied to the Korteweg-de Vries and Korteweg-de Vries-Burger’s equations.) Zbl 1432.35229
Saad, Khaled M.; Baleanu, Dumitru; Atangana, Abdon
2018
Controlling the wave movement on the surface of shallow water with the Caputo-Fabrizio derivative with fractional order. Zbl 1360.35164
Alkahtani, B. S. T.; Atangana, A.
2016
Modeling attractors of chaotic dynamical systems with fractal-fractional operators. Zbl 1448.65268
Atangana, Abdon; Qureshi, Sania
2019
Numerical approximation of the space-time Caputo-Fabrizio fractional derivative and application to groundwater pollution equation. Zbl 1422.65144
Atangana, Abdon; Alqahtani, Rubayyi T.
2016
A generalized groundwater flow equation using the concept of variable-order derivative. Zbl 1291.35206
Atangana, Abdon; Botha, Joseph
2013
Nonlinear fractional Jaulent-Miodek and Whitham-Broer-Kaup equations within Sumudu transform. Zbl 1275.65066
Atangana, Abdon; Baleanu, Dumitru
2013
Robustness of fractional difference schemes via the Caputo subdiffusion-reaction equations. Zbl 1395.65026
2018
Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws. Zbl 1415.65148
Solís-Pérez, J. E.; Gómez-Aguilar, J. F.; Atangana, A.
2018
On generalized fractional kinetic equations involving generalized Bessel function of the first kind. Zbl 1394.34018
Kumar, Dinesh; Purohit, S. D.; Secer, A.; Atangana, A.
2015
Stability and convergence of the space fractional variable-order Schrödinger equation. Zbl 1380.35157
Atangana, Abdon; Cloot, Alain H.
2013
Derivative with a new parameter. Theory, methods and applications. Zbl 1342.26020
Atangana, Abdon
2016
Retracted: New numerical method for ordinary differential equations: Newton polynomial. Zbl 1453.65152
Atangana, Abdon; İğret Araz, Seda
2020
Chaotic behaviour in system of noninteger-order ordinary differential equations. Zbl 1416.65180
2018
Fractional operators with constant and variable order with application to geo-hydrology. Zbl 1386.86001
Atangana, Abdon
2018
Fractional stochastic modeling: new approach to capture more heterogeneity. Zbl 1406.37044
Atangana, A.; Bonyah, E.
2019
Retracted: A fractional model for predator-prey with omnivore. Zbl 1406.92652
Bonyah, E.; Atangana, A.; Elsadany, A. A.
2019
Numerical simulations of chaotic and complex spatiotemporal patterns in fractional reaction-diffusion systems. Zbl 06912510
2018
Analytical solutions of the space-time fractional derivative of advection dispersion equation. Zbl 1299.35058
2013
The use of fractional order derivative to predict the groundwater flow. Zbl 1296.76144
Atangana, Abdon; Bildik, Necdet
2013
Numerical methods for fractional differentiation. Zbl 1429.65005
2019
Extension of matched asymptotic method to fractional boundary layers problems. Zbl 1407.34005
Atangana, Abdon; Doungmo Goufo, Emile Franc
2014
Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators. Zbl 1412.34059
2017
Couette flows of a viscous fluid with slip effects and non-integer order derivative without singular kernel. Zbl 1418.35312
2019
A novel approach of variable order derivative theory and methods. Zbl 1350.26009
2016
Analytical solutions of a space-time fractional derivative of groundwater flow equation. Zbl 1468.35225
Atangana, Abdon; Vermeulen, P. D.
2014
New two step Laplace Adam-Bashforth method for integer a noninteger order partial differential equations. Zbl 1407.65242
Gnitchogna, Rodrigue; Atangana, Abdon
2018
The use of Sumudu transform for solving certain nonlinear fractional heat-like equations. Zbl 1275.65067
2013
Model of thin viscous fluid sheet flow within the scope of fractional calculus: fractional derivative with and no singular kernel. Zbl 1375.76020
Atangana, Abdon; Koca, Ilknur
2017
A meshless approach for solving nonlinear variable-order time fractional 2D Ginzburg-Landau equation. Zbl 1464.65143
Heydari, M. H.; Hosseininia, M.; Atangana, A.; Avazzadeh, Z.
2020
On multi-Laplace transform for solving nonlinear partial differential equations with mixed derivatives. Zbl 1407.35058
Atangana, Abdon; Oukouomi Noutchie, Suares Clovis
2014
A possible generalization of acoustic wave equation using the concept of perturbed derivative order. Zbl 1299.76229
2013
Stability and convergence of a time-fractional variable order Hantush equation for a deformable aquifer. Zbl 1301.76072
Atangana, Abdon; Oukouomi Noutchie, S. C.
2013
Validity of fractal derivative to capturing chaotic attractors. Zbl 1448.34010
2019
Numerical solution of a kind of fractional parabolic equations via two difference schemes. Zbl 1470.65148
Atangana, Abdon; Baleanu, Dumitru
2013
Capturing complexities with composite operator and differential operators with non-singular kernel. Zbl 07034126
Atangana, Abdon; Mekkaoui, Toufik
2019
Existence and numerical solution of the Volterra fractional integral equations of the second kind. Zbl 1299.45001
Atangana, Abdon; Bildik, Necdet
2013
Mathematical analysis and numerical simulation of two-component system with non-integer-order derivative in high dimensions. Zbl 1422.35168
2017
A numerical study of the nonlinear fractional mathematical model of tumor cells in presence of chemotherapeutic treatment. Zbl 1443.92101
Kumar, Sachin; Atangana, Abdon
2020
A fractional mathematical model of breast cancer competition model. Zbl 1448.92105
Solís-Pérez, J. E.; Gómez-Aguilar, J. F.; Atangana, A.
2019
New lump, lump-kink, breather waves and other interaction solutions to the $$(3+1)$$-dimensional soliton equation. Zbl 1451.35052
Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Atangana, Abdon
2020
Solving partial differential equation with space- and time-fractional derivatives via homotopy decomposition method. Zbl 1296.35010
Atangana, Abdon; Belhaouari, Samir Brahim
2013
A new model of groundwater flow within an unconfined aquifer: application of Caputo-Fabrizio fractional derivative. Zbl 1416.76175
Feulefack, Pierre Aime; Djida, Jean Daniel; Abdon, Atangana
2019
A note on the triple Laplace transform and its applications to some kind of third-order differential equation. Zbl 1470.44001
Atangana, Abdon
2013
A generalized version of a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate using the concept of noninteger derivatives. Zbl 1364.74039
Atangana, Abdon; Ahmed, O. Aden; Bıldık, Necdet
2013
Analysis of a new partial integro-differential equation with mixed fractional operators. Zbl 1448.65277
Atangana, Abdon; Araz, Seda İğret
2019
Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative. Zbl 1448.34022
2019
A new approach to capture heterogeneity in groundwater problem: an illustration with an Earth equation. Zbl 1470.76096
Atangana, Abdon; Alqahtani, Rubayyi T.
2019
High-order solvers for space-fractional differential equations with Riesz derivative. Zbl 1422.65179
2019
Mathematical analysis of memristor through fractal-fractional differential operators: a numerical study. Zbl 1455.34048
Abro, Kashif Ali; Atangana, Abdon
2020
Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method. Zbl 1291.35026
2013
A model of the groundwater flowing within a leaky aquifer using the concept of local variable order derivative. Zbl 1330.76128
Atangana, Abdon; Goufo, Emile Franc Doungmo
2015
Analytical solution of space-time fractional Fokker-Planck equation by homotopy perturbation Sumudu transform method. Zbl 1394.35075
2015
First integral method for non-linear differential equations with conformable derivative. Zbl 1458.35463
Yépez-Martínez, H.; Gómez-Aguilar, J. F.; Atangana, Abdon
2018
Editorial: Fractional differential and integral operators with non-singular and non-local kernel with application to nonlinear dynamical systems. Zbl 1434.00041
2020
Conservatory of Kaup-Kupershmidt equation to the concept of fractional derivative with and without singular kernel. Zbl 1393.35198
Atangana, Abdon; Goufo, Emile Franc Doungmo
2018
Huge analysis of Hepatitis C model within the scope of fractional calculus. Zbl 1381.34065
2016
A novel integral operator transform and its application to some FODE and FPDE with some kind of singularities. Zbl 1296.44001
2013
New numerical method and application to Keller-Segel model with fractional order derivative. Zbl 1442.35499
Atangana, Abdon; Alqahtani, Rubayyi T.
2018
Approximate solution of tuberculosis disease population dynamics model. Zbl 1470.92015
Atangana, Abdon; Bildik, Necdet
2013
Generalised class of time fractional black Scholes equation and numerical analysis. Zbl 1422.91680
Batogna, Rodrigue Gnitchogna; Atangana, Abdon
2019
Error estimates of a semidiscrete finite element method for fractional stochastic diffusion-wave equations. Zbl 1407.74098
Zou, Guang-an; Atangana, Abdon; Zhou, Yong
2018
More generalized groundwater model with space-time Caputo Fabrizio fractional differentiation. Zbl 1394.65071
Djida, Jean-Daniel; Atangana, Abdon
2017
Analysis of Lassa hemorrhagic fever model with non-local and non-singular fractional derivatives. Zbl 1405.92256
Jain, Sonal; Atangana, Abdon
2018
Augmented upwind numerical schemes for a fractional advection-dispersion equation in fractured groundwater systems. Zbl 07200451
Allwright, Amy; Atangana, Abdon
2020
Dynamics of traveling waves of variable order hyperbolic Liouville equation: regulation and control. Zbl 1439.35118
Goufo, Emile Franc Doungmo; Atangana, Abdon
2020
Differential and integral operators with constant fractional order and variable fractional dimension. Zbl 1448.34011
Atangana, Abdon; Shafiq, Anum
2019
On the solution of an acoustic wave equation with variable-order derivative loss operator. Zbl 1444.65047
Atangana, Abdon
2013
New iteration methods for time-fractional modified nonlinear Kawahara equation. Zbl 1474.35635
Atangana, Abdon; Bildik, Necdet; Noutchie, S. C. Oukouomi
2014
On the stability of iteration methods for special solution of time-fractional generalized nonlinear ZK-BBM equation. Zbl 1365.35198
Atangana, Abdon
2016
A novel double integral transform and its applications. Zbl 1327.31009
2016
Analysis of a nonlinear model of interpersonal relationships with time fractional derivative. Zbl 1362.34015
Koca, Ilknur; Atangana, Abdon
2016
Extension of the Sumudu homotopy perturbation method to an attractor for one-dimensional Keller-Segel equations. Zbl 1443.65267
Atangana, Abdon
2015
An optimization method based on the generalized Lucas polynomials for variable-order space-time fractional mobile-immobile advection-dispersion equation involving derivatives with non-singular kernels. Zbl 1434.35274
Heydari, M. H.; Atangana, A.
2020
On the dynamics of fractional maps with power-law, exponential decay and Mittag-Leffler memory. Zbl 1448.34086
Ávalos-Ruiz, L. F.; Gómez-Aguilar, J. F.; Atangana, A.; Owolabi, Kolade M.
2019
A comparative analysis of electromechanical model of piezoelectric actuator through Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. Zbl 1456.35207
Abro, Kashif Ali; Atangana, Abdon
2020
Orthonormal shifted discrete Legendre polynomials for solving a coupled system of nonlinear variable-order time fractional reaction-advection-diffusion equations. Zbl 1461.65246
Heydari, M. H.; Avazzadeh, Z.; Atangana, A.
2021
New numerical analysis of Riemann-Liouville time-fractional Schrödinger with power, exponential decay, and Mittag-Leffler laws. Zbl 1415.65181
2017
Derivation of a groundwater flow model within leaky and self-similar aquifers: beyond Hantush model. Zbl 1442.76108
Amanda, Ramotsho; Atangana, Abdon
2018
Orthonormal shifted discrete Legendre polynomials for solving a coupled system of nonlinear variable-order time fractional reaction-advection-diffusion equations. Zbl 1461.65246
Heydari, M. H.; Avazzadeh, Z.; Atangana, A.
2021
New numerical scheme with Newton polynomial. Theory, methods, and applications. Zbl 1462.65001
Atangana, Abdon; İğret Araz, Seda
2021
Numerical solution of nonlinear fractal-fractional optimal control problems by Legendre polynomials. Zbl 07376715
2021
Shifted Vieta-Fibonacci polynomials for the fractal-fractional fifth-order KdV equation. Zbl 1473.35485
Heydari, M. H.; Avazzadeh, Z.; Atangana, A.
2021
On solutions of fractal fractional differential equations. Zbl 1481.34009
Atangana, Abdon; Akgül, Ali
2021
Retracted: New numerical method for ordinary differential equations: Newton polynomial. Zbl 1453.65152
Atangana, Abdon; İğret Araz, Seda
2020
A meshless approach for solving nonlinear variable-order time fractional 2D Ginzburg-Landau equation. Zbl 1464.65143
Heydari, M. H.; Hosseininia, M.; Atangana, A.; Avazzadeh, Z.
2020
A numerical study of the nonlinear fractional mathematical model of tumor cells in presence of chemotherapeutic treatment. Zbl 1443.92101
Kumar, Sachin; Atangana, Abdon
2020
New lump, lump-kink, breather waves and other interaction solutions to the $$(3+1)$$-dimensional soliton equation. Zbl 1451.35052
Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Atangana, Abdon
2020
Mathematical analysis of memristor through fractal-fractional differential operators: a numerical study. Zbl 1455.34048
Abro, Kashif Ali; Atangana, Abdon
2020
Editorial: Fractional differential and integral operators with non-singular and non-local kernel with application to nonlinear dynamical systems. Zbl 1434.00041
2020
Augmented upwind numerical schemes for a fractional advection-dispersion equation in fractured groundwater systems. Zbl 07200451
Allwright, Amy; Atangana, Abdon
2020
Dynamics of traveling waves of variable order hyperbolic Liouville equation: regulation and control. Zbl 1439.35118
Goufo, Emile Franc Doungmo; Atangana, Abdon
2020
An optimization method based on the generalized Lucas polynomials for variable-order space-time fractional mobile-immobile advection-dispersion equation involving derivatives with non-singular kernels. Zbl 1434.35274
Heydari, M. H.; Atangana, A.
2020
A comparative analysis of electromechanical model of piezoelectric actuator through Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. Zbl 1456.35207
Abro, Kashif Ali; Atangana, Abdon
2020
Models of fluid flowing in non-conventional media: new numerical analysis. Zbl 1440.65082
Atangana, Abdon; Jain, Sonal
2020
Solving fractional pantograph delay equations by an effective computational method. Zbl 07318101
Hashemi, M. S.; Atangana, A.; Hajikhah, S.
2020
Mathematical model of COVID-19 spread in Turkey and south Africa: theory, methods, and applications. Zbl 07485377
Atangana, Abdon; İğret Araz, Seda
2020
Fractional order analysis. Theory, methods and applications. Zbl 1445.26001
2020
Corrigendum to: “New numerical method for ordinary differential equations: Newton polynomial”. Zbl 1453.65151
Atangana, Abdon; Araz, Seda İğret
2020
Cauchy problems with fractal-fractional operators and applications to groundwater dynamics. Zbl 1483.35315
Atangana, Abdon; Doungmo Goufo, Emile Franc
2020
Atangana-Seda numerical scheme for labyrinth attractor with new differential and integral operators. Zbl 07468626
Atangana, Abdon; İğret Araz, Seda
2020
Optimal control for cancer treatment mathematical model using Atangana-Baleanu-Caputo fractional derivative. Zbl 07490983
Sweilam, Nasser Hassan; Al-Mekhlafi, Seham Mahyoub; Assiri, Taghreed; Atangana, Abdon
2020
On the formulation of Adams-bashforth scheme with Atangana-Baleanu-Caputo fractional derivative to model chaotic problems. Zbl 1409.34016
2019
Modeling attractors of chaotic dynamical systems with fractal-fractional operators. Zbl 1448.65268
Atangana, Abdon; Qureshi, Sania
2019
Fractional stochastic modeling: new approach to capture more heterogeneity. Zbl 1406.37044
Atangana, A.; Bonyah, E.
2019
Retracted: A fractional model for predator-prey with omnivore. Zbl 1406.92652
Bonyah, E.; Atangana, A.; Elsadany, A. A.
2019
Numerical methods for fractional differentiation. Zbl 1429.65005
2019
Couette flows of a viscous fluid with slip effects and non-integer order derivative without singular kernel. Zbl 1418.35312
2019
Validity of fractal derivative to capturing chaotic attractors. Zbl 1448.34010
2019
Capturing complexities with composite operator and differential operators with non-singular kernel. Zbl 07034126
Atangana, Abdon; Mekkaoui, Toufik
2019
A fractional mathematical model of breast cancer competition model. Zbl 1448.92105
Solís-Pérez, J. E.; Gómez-Aguilar, J. F.; Atangana, A.
2019
A new model of groundwater flow within an unconfined aquifer: application of Caputo-Fabrizio fractional derivative. Zbl 1416.76175
Feulefack, Pierre Aime; Djida, Jean Daniel; Abdon, Atangana
2019
Analysis of a new partial integro-differential equation with mixed fractional operators. Zbl 1448.65277
Atangana, Abdon; Araz, Seda İğret
2019
Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative. Zbl 1448.34022
2019
A new approach to capture heterogeneity in groundwater problem: an illustration with an Earth equation. Zbl 1470.76096
Atangana, Abdon; Alqahtani, Rubayyi T.
2019
High-order solvers for space-fractional differential equations with Riesz derivative. Zbl 1422.65179
2019
Generalised class of time fractional black Scholes equation and numerical analysis. Zbl 1422.91680
Batogna, Rodrigue Gnitchogna; Atangana, Abdon
2019
Differential and integral operators with constant fractional order and variable fractional dimension. Zbl 1448.34011
Atangana, Abdon; Shafiq, Anum
2019
On the dynamics of fractional maps with power-law, exponential decay and Mittag-Leffler memory. Zbl 1448.34086
Ávalos-Ruiz, L. F.; Gómez-Aguilar, J. F.; Atangana, A.; Owolabi, Kolade M.
2019
RETRACTED: Power and exponentials laws: theory and application. Zbl 1423.26011
Gómez-Aguilar, J. F.; Atangana, Abdon
2019
Necessary and sufficient optimality conditions for fractional problems involving Atangana-Baleanu’s derivatives. Zbl 1436.49032
Bahaa, G. M.; Atangana, A.
2019
Modulating chaotic oscillations in autocatalytic reaction networks using Atangana-Baleanu operator. Zbl 1448.92076
Goufo, Emile F. Doungmo; Atangana, A.
2019
Upwind-based numerical approximation of a space-time fractional advection-dispersion equation for groundwater transport within fractured systems. Zbl 1440.76141
Allwright, A.; Atangana, A.
2019
A fractional epidemiological model for computer viruses pertaining to a new fractional derivative. Zbl 1426.68015
Singh, Jagdev; Kumar, Devendra; Hammouch, Zakia; Atangana, Abdon
2018
Fractional derivatives with no-index law property: application to chaos and statistics. Zbl 1415.34010
Atangana, Abdon; Gómez-Aguilar, J. F.
2018
New numerical approach for fractional differential equations. Zbl 1406.65045
2018
Numerical approximation of Riemann-Liouville definition of fractional derivative: from Riemann-Liouville to Atangana-Baleanu. Zbl 1417.65113
Atangana, Abdon; Gómez-aguilar, J. F.
2018
Blind in a commutative world: simple illustrations with functions and chaotic attractors. Zbl 1415.34009
Atangana, Abdon
2018
New fractional derivatives with non-singular kernel applied to the Burgers equation. Zbl 1394.35565
Saad, Khaled M.; Atangana, Abdon; Baleanu, Dumitru
2018
New fractional derivatives applied to the Korteweg-de Vries and Korteweg-de Vries-Burgers equations. (New fractional derivatives applied to the Korteweg-de Vries and Korteweg-de Vries-Burger’s equations.) Zbl 1432.35229
Saad, Khaled M.; Baleanu, Dumitru; Atangana, Abdon
2018
Robustness of fractional difference schemes via the Caputo subdiffusion-reaction equations. Zbl 1395.65026
2018
Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws. Zbl 1415.65148
Solís-Pérez, J. E.; Gómez-Aguilar, J. F.; Atangana, A.
2018
Chaotic behaviour in system of noninteger-order ordinary differential equations. Zbl 1416.65180
2018
Fractional operators with constant and variable order with application to geo-hydrology. Zbl 1386.86001
Atangana, Abdon
2018
Numerical simulations of chaotic and complex spatiotemporal patterns in fractional reaction-diffusion systems. Zbl 06912510
2018
New two step Laplace Adam-Bashforth method for integer a noninteger order partial differential equations. Zbl 1407.65242
Gnitchogna, Rodrigue; Atangana, Abdon
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
Conservatory of Kaup-Kupershmidt equation to the concept of fractional derivative with and without singular kernel. Zbl 1393.35198
Atangana, Abdon; Goufo, Emile Franc Doungmo
2018
New numerical method and application to Keller-Segel model with fractional order derivative. Zbl 1442.35499
Atangana, Abdon; Alqahtani, Rubayyi T.
2018
Error estimates of a semidiscrete finite element method for fractional stochastic diffusion-wave equations. Zbl 1407.74098
Zou, Guang-an; Atangana, Abdon; Zhou, Yong
2018
Analysis of Lassa hemorrhagic fever model with non-local and non-singular fractional derivatives. Zbl 1405.92256
Jain, Sonal; Atangana, Abdon
2018
Derivation of a groundwater flow model within leaky and self-similar aquifers: beyond Hantush model. Zbl 1442.76108
Amanda, Ramotsho; Atangana, Abdon
2018
Solitary wave solution and conservation laws of higher dimensional Zakharov-Kuznetsov equation with nonlinear self-adjointness. Zbl 1402.74056
2018
Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Zbl 1374.28002
Atangana, Abdon
2017
Analysis and application of new fractional Adams-Bashforth scheme with Caputo-Fabrizio derivative. Zbl 1380.65120
2017
Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws. Zbl 1374.34296
Atangana, Abdon; Gómez-Aguilar, J. F.
2017
Numerical computation of a fractional derivative with non-local and non-singular kernel. Zbl 1416.65190
Djida, Jean Daniel; Atangana, A.; Area, I.
2017
Numerical approximation of nonlinear fractional parabolic differential equations with Caputo-Fabrizio derivative in Riemann-Liouville sense. Zbl 1422.65178
2017
Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators. Zbl 1412.34059
2017
Model of thin viscous fluid sheet flow within the scope of fractional calculus: fractional derivative with and no singular kernel. Zbl 1375.76020
Atangana, Abdon; Koca, Ilknur
2017
Mathematical analysis and numerical simulation of two-component system with non-integer-order derivative in high dimensions. Zbl 1422.35168
2017
More generalized groundwater model with space-time Caputo Fabrizio fractional differentiation. Zbl 1394.65071
Djida, Jean-Daniel; Atangana, Abdon
2017
New numerical analysis of Riemann-Liouville time-fractional Schrödinger with power, exponential decay, and Mittag-Leffler laws. Zbl 1415.65181
2017
Modelling the movement of groundwater pollution with variable order derivative. Zbl 1412.34031
Kameni, S. N.; Djida, J. D.; Atangana, A.
2017
Numerical analysis for the Klein-Gordon equation with mass parameter. Zbl 1444.65046
2017
Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order. Zbl 1360.34150
Atangana, Abdon; Koca, Ilknur
2016
On the new fractional derivative and application to nonlinear Fisher’s reaction-diffusion equation. Zbl 1410.35272
Atangana, Abdon
2016
On the new fractional derivative and application to nonlinear Baggs and Freedman model. Zbl 1335.34079
Atangana, Abdon; Koca, Ilknur
2016
Analysis of non-homogeneous heat model with new trend of derivative with fractional order. Zbl 1360.35080
2016
Controlling the wave movement on the surface of shallow water with the Caputo-Fabrizio derivative with fractional order. Zbl 1360.35164
Alkahtani, B. S. T.; Atangana, A.
2016
Numerical approximation of the space-time Caputo-Fabrizio fractional derivative and application to groundwater pollution equation. Zbl 1422.65144
Atangana, Abdon; Alqahtani, Rubayyi T.
2016
Derivative with a new parameter. Theory, methods and applications. Zbl 1342.26020
Atangana, Abdon
2016
A novel approach of variable order derivative theory and methods. Zbl 1350.26009
2016
Huge analysis of Hepatitis C model within the scope of fractional calculus. Zbl 1381.34065
2016
On the stability of iteration methods for special solution of time-fractional generalized nonlinear ZK-BBM equation. Zbl 1365.35198
Atangana, Abdon
2016
A novel double integral transform and its applications. Zbl 1327.31009
2016
Analysis of a nonlinear model of interpersonal relationships with time fractional derivative. Zbl 1362.34015
Koca, Ilknur; Atangana, Abdon
2016
Exact solution of the time-fractional groundwater flow equation within a leaky aquifer equation. Zbl 1365.35197
Atangana, Abdon
2016
New properties of conformable derivative. Zbl 1354.26008
Atangana, Abdon; Baleanu, Dumitru; Alsaedi, Ahmed
2015
Analysis of the Keller-Segel model with a fractional derivative without singular kernel. Zbl 1338.35458
2015
On the stability and convergence of the time-fractional variable order telegraph equation. Zbl 1349.65263
Atangana, Abdon
2015
On generalized fractional kinetic equations involving generalized Bessel function of the first kind. Zbl 1394.34018
Kumar, Dinesh; Purohit, S. D.; Secer, A.; Atangana, A.
2015
A model of the groundwater flowing within a leaky aquifer using the concept of local variable order derivative. Zbl 1330.76128
Atangana, Abdon; Goufo, Emile Franc Doungmo
2015
Analytical solution of space-time fractional Fokker-Planck equation by homotopy perturbation Sumudu transform method. Zbl 1394.35075
2015
Extension of the Sumudu homotopy perturbation method to an attractor for one-dimensional Keller-Segel equations. Zbl 1443.65267
Atangana, Abdon
2015
Extension of matched asymptotic method to fractional boundary layers problems. Zbl 1407.34005
Atangana, Abdon; Doungmo Goufo, Emile Franc
2014
Analytical solutions of a space-time fractional derivative of groundwater flow equation. Zbl 1468.35225
Atangana, Abdon; Vermeulen, P. D.
2014
On multi-Laplace transform for solving nonlinear partial differential equations with mixed derivatives. Zbl 1407.35058
Atangana, Abdon; Oukouomi Noutchie, Suares Clovis
2014
New iteration methods for time-fractional modified nonlinear Kawahara equation. Zbl 1474.35635
Atangana, Abdon; Bildik, Necdet; Noutchie, S. C. Oukouomi
2014
...and 26 more Documents
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### Cited in 179 Serials

 266 Chaos, Solitons and Fractals 115 Advances in Difference Equations 50 Fractals 46 Discrete and Continuous Dynamical Systems. Series S 40 Abstract and Applied Analysis 36 Journal of Function Spaces 33 AIMS Mathematics 27 Applied Mathematics and Computation 26 Chaos 25 International Journal of Applied and Computational Mathematics 23 Applied Numerical Mathematics 22 Mathematical Modelling of Natural Phenomena 22 Journal of Nonlinear Science and Applications 21 Computational and Applied Mathematics 21 Advances in Mathematical Physics 19 Mathematical Problems in Engineering 18 Journal of Computational and Applied Mathematics 13 International Journal of Biomathematics 12 Mathematics and Computers in Simulation 11 Nonlinear Dynamics 10 Journal of Applied Analysis and Computation 10 Open Mathematics 9 Complexity 8 Physica A 8 Applied Mathematical Modelling 8 Boundary Value Problems 7 Computers & Mathematics with Applications 7 Applied Mathematics Letters 7 Numerical Algorithms 7 International Journal of Computer Mathematics 7 Discrete Dynamics in Nature and Society 7 Communications in Nonlinear Science and Numerical Simulation 7 Journal of Mathematics 6 Journal of Computational Physics 6 International Journal of Nonlinear Sciences and Numerical Simulation 5 Journal of Applied Mathematics and Computing 5 International Journal of Differential Equations 5 Symmetry 4 Journal of the Franklin Institute 4 Mathematical Modelling and Analysis 4 Mathematical Biosciences and Engineering 4 Inverse Problems in Science and Engineering 4 Mathematical Sciences 3 Journal of Geometry and Physics 3 Applied Mathematics. Series B (English Edition) 3 Engineering Analysis with Boundary Elements 3 Journal of Inequalities and Applications 3 European Journal of Pure and Applied Mathematics 3 Arabian Journal of Mathematics 3 International Journal of Systems Science. Principles and Applications of Systems and Integration 3 Electronic Research Archive 2 International Journal of Modern Physics B 2 Acta Mechanica 2 Journal of Mathematical Physics 2 Mathematical Biosciences 2 Rocky Mountain Journal of Mathematics 2 Journal of Optimization Theory and Applications 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Journal of the Egyptian Mathematical Society 2 Filomat 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Journal of Vibration and Control 2 Fractional Calculus & Applied Analysis 2 European Journal of Mechanics. B. Fluids 2 Russian Physics Journal 2 Nonlinear Analysis. Modelling and Control 2 Journal of Applied Mathematics 2 Thai Journal of Mathematics 2 Boletim da Sociedade Paranaense de Matemática. Terceira Série 2 Journal of Statistical Mechanics: Theory and Experiment 2 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 2 The Journal of Prime Research in Mathematics 2 Applications and Applied Mathematics 2 Communications in Theoretical Physics 2 Journal of Mathematics and Computer Science. JMCS 2 Analysis and Mathematical Physics 2 Journal of Mathematical Extension 2 S$$\vec{\text{e}}$$MA Journal 2 Palestine Journal of Mathematics 2 Evolution Equations and Control Theory 2 International Journal of Analysis and Applications 2 Iranian Journal of Numerical Analysis and Optimization 2 Computational Methods for Differential Equations 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Waves, Wavelets and Fractals. Advanced Analysis 2 Transactions of A. Razmadze Mathematical Institute 1 Archives of Mechanics 1 Computer Physics Communications 1 Indian Journal of Pure & Applied Mathematics 1 Mathematical Methods in the Applied Sciences 1 Nonlinearity 1 Periodica Mathematica Hungarica 1 Physics Letters. A 1 Reports on Mathematical Physics 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 International Journal of Mathematics and Mathematical Sciences 1 The Journal of Mathematical Sociology 1 Kyungpook Mathematical Journal 1 Numerische Mathematik 1 Quaestiones Mathematicae ...and 79 more Serials
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### Cited in 47 Fields

 492 Partial differential equations (35-XX) 475 Ordinary differential equations (34-XX) 397 Numerical analysis (65-XX) 362 Real functions (26-XX) 228 Biology and other natural sciences (92-XX) 80 Fluid mechanics (76-XX) 72 Dynamical systems and ergodic theory (37-XX) 57 Systems theory; control (93-XX) 56 Special functions (33-XX) 49 Operator theory (47-XX) 48 Integral equations (45-XX) 41 Integral transforms, operational calculus (44-XX) 38 Difference and functional equations (39-XX) 31 Calculus of variations and optimal control; optimization (49-XX) 26 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 23 Mechanics of deformable solids (74-XX) 21 Statistical mechanics, structure of matter (82-XX) 18 Geophysics (86-XX) 16 Probability theory and stochastic processes (60-XX) 14 Measure and integration (28-XX) 13 Approximations and expansions (41-XX) 12 Mechanics of particles and systems (70-XX) 12 Operations research, mathematical programming (90-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 9 Computer science (68-XX) 9 Optics, electromagnetic theory (78-XX) 9 Quantum theory (81-XX) 8 Classical thermodynamics, heat transfer (80-XX) 8 Information and communication theory, circuits (94-XX) 7 Functional analysis (46-XX) 7 General topology (54-XX) 5 Statistics (62-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Functions of a complex variable (30-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Potential theory (31-XX) 2 Sequences, series, summability (40-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 Algebraic topology (55-XX) 1 Mathematics education (97-XX)

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