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Van Dac, Nguyen; Dinh, Ke Tran; Thuy, Lam Tran Phuong On stability and regularity for semilinear anomalous diffusion equations perturbed by weak-valued nonlinearities. (English) Zbl 1527.35083 Discrete Contin. Dyn. Syst., Ser. S 16, No. 10, 2883-2901 (2023). MSC: 35B40 35B65 35C15 35K20 35R11 45D05 45K05 PDFBibTeX XMLCite \textit{N. Van Dac} et al., Discrete Contin. Dyn. Syst., Ser. S 16, No. 10, 2883--2901 (2023; Zbl 1527.35083) Full Text: DOI
Chowdhury, Indranil; Ersland, Olav; Jakobsen, Espen R. On numerical approximations of fractional and nonlocal mean field games. (English) Zbl 1527.35428 Found. Comput. Math. 23, No. 4, 1381-1431 (2023). MSC: 35Q89 35Q84 91A16 47G20 49L12 49L25 45K05 35K61 35F21 65M12 65M22 93B52 93C20 60J65 60G55 26A33 35R11 35R06 PDFBibTeX XMLCite \textit{I. Chowdhury} et al., Found. Comput. Math. 23, No. 4, 1381--1431 (2023; Zbl 1527.35428) Full Text: DOI arXiv
Alegría, Francisco; Poblete, Verónica; Pozo, Juan C. Nonlocal in-time telegraph equation and telegraph processes with random time. (English) Zbl 1505.35346 J. Differ. Equations 347, 310-347 (2023). MSC: 35R11 35R60 26A33 45D05 60G22 60H15 60H20 PDFBibTeX XMLCite \textit{F. Alegría} et al., J. Differ. Equations 347, 310--347 (2023; Zbl 1505.35346) Full Text: DOI
D’Elia, Marta; Glusa, Christian A fractional model for anomalous diffusion with increased variability: analysis, algorithms and applications to interface problems. (English) Zbl 07779691 Numer. Methods Partial Differ. Equations 38, No. 6, 2084-2103 (2022). MSC: 65N30 65N12 35J05 35B65 47N20 45P05 31C25 35A01 35A02 26A33 35R11 35R99 PDFBibTeX XMLCite \textit{M. D'Elia} and \textit{C. Glusa}, Numer. Methods Partial Differ. Equations 38, No. 6, 2084--2103 (2022; Zbl 07779691) Full Text: DOI arXiv
D’Elia, Marta; Gulian, Mamikon Analysis of anisotropic nonlocal diffusion models: well-posedness of fractional problems for anomalous transport. (English) Zbl 07672281 Numer. Math., Theory Methods Appl. 15, No. 4, 851-875 (2022). MSC: 60K50 60G22 60H20 45R05 PDFBibTeX XMLCite \textit{M. D'Elia} and \textit{M. Gulian}, Numer. Math., Theory Methods Appl. 15, No. 4, 851--875 (2022; Zbl 07672281) Full Text: DOI arXiv
Bouin, Émeric; Mouhot, Clément Quantitative fluid approximation in transport theory: a unified approach. (English) Zbl 1511.35348 Probab. Math. Phys. 3, No. 3, 491-542 (2022). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q84 35Q35 76P05 82C40 82C70 82D05 26A33 35A23 35R11 45A05 60K50 35P25 60G51 60J65 PDFBibTeX XMLCite \textit{É. Bouin} and \textit{C. Mouhot}, Probab. Math. Phys. 3, No. 3, 491--542 (2022; Zbl 1511.35348) Full Text: DOI arXiv
Bender, Christian; Butko, Yana A. Stochastic solutions of generalized time-fractional evolution equations. (English) Zbl 1503.45005 Fract. Calc. Appl. Anal. 25, No. 2, 488-519 (2022). MSC: 45J05 45R05 60H20 26A33 33E12 60G22 60G65 33C65 PDFBibTeX XMLCite \textit{C. Bender} and \textit{Y. A. Butko}, Fract. Calc. Appl. Anal. 25, No. 2, 488--519 (2022; Zbl 1503.45005) Full Text: DOI arXiv
Lee, Hwi; Du, Qiang Second-order accurate Dirichlet boundary conditions for linear nonlocal diffusion problems. (English) Zbl 1499.34142 Commun. Math. Sci. 20, No. 7, 1815-1837 (2022). MSC: 34B10 35A01 35B40 45A05 60K50 65N12 74A70 PDFBibTeX XMLCite \textit{H. Lee} and \textit{Q. Du}, Commun. Math. Sci. 20, No. 7, 1815--1837 (2022; Zbl 1499.34142) Full Text: DOI arXiv
Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil The two-phase Stefan problem with anomalous diffusion. (English) Zbl 1495.35176 Adv. Math. 406, Article ID 108527, 19 p. (2022). MSC: 35R09 35R11 35R35 45K05 80A22 PDFBibTeX XMLCite \textit{I. Athanasopoulos} et al., Adv. Math. 406, Article ID 108527, 19 p. (2022; Zbl 1495.35176) Full Text: DOI arXiv
Okrasińska-Płociniczak, Hanna; Płociniczak, Łukasz Second order scheme for self-similar solutions of a time-fractional porous medium equation on the half-line. (English) Zbl 1510.35383 Appl. Math. Comput. 424, Article ID 127033, 19 p. (2022). MSC: 35R11 45G10 65R20 PDFBibTeX XMLCite \textit{H. Okrasińska-Płociniczak} and \textit{Ł. Płociniczak}, Appl. Math. Comput. 424, Article ID 127033, 19 p. (2022; Zbl 1510.35383) Full Text: DOI arXiv
Van Bockstal, Karel Existence of a unique weak solution to a non-autonomous time-fractional diffusion equation with space-dependent variable order. (English) Zbl 1494.35170 Adv. Difference Equ. 2021, Paper No. 314, 43 p. (2021). MSC: 35R11 26A33 45K05 65R20 PDFBibTeX XMLCite \textit{K. Van Bockstal}, Adv. Difference Equ. 2021, Paper No. 314, 43 p. (2021; Zbl 1494.35170) Full Text: DOI
Tran, Dinh-Ke; Lam, Tran-Phuong-Thuy Nonlocal final value problem governed by semilinear anomalous diffusion equations. (English) Zbl 1455.35302 Evol. Equ. Control Theory 9, No. 3, 891-914 (2020). MSC: 35R30 35K20 35R09 45D05 45K05 PDFBibTeX XMLCite \textit{D.-K. Tran} and \textit{T.-P.-T. Lam}, Evol. Equ. Control Theory 9, No. 3, 891--914 (2020; Zbl 1455.35302) Full Text: DOI
Maleknejad, Khosrow; Dehbozorgi, Raziyeh; Garshasbi, Morteza Direct operational matrix approach for weakly singular Volterra integro-differential equations: application in theory of anomalous diffusion. (English) Zbl 1418.65199 Math. Commun. 24, No. 1, 61-76 (2019). MSC: 65R20 45J05 45E10 PDFBibTeX XMLCite \textit{K. Maleknejad} et al., Math. Commun. 24, No. 1, 61--76 (2019; Zbl 1418.65199) Full Text: Link
Yang, Zongze; Wang, Jungang; Li, Yan; Nie, Yufeng Effective numerical treatment of sub-diffusion equation with non-smooth solution. (English) Zbl 1499.35694 Int. J. Comput. Math. 95, No. 6-7, 1394-1407 (2018). MSC: 35R11 65M70 45D05 PDFBibTeX XMLCite \textit{Z. Yang} et al., Int. J. Comput. Math. 95, No. 6--7, 1394--1407 (2018; Zbl 1499.35694) Full Text: DOI arXiv
Padrino, Juan C. On the self-similar, Wright-function exact solution for early-time, anomalous diffusion in random networks: comparison with numerical results. (English) Zbl 1400.82252 Int. J. Appl. Comput. Math. 4, No. 5, Paper No. 131, 10 p. (2018). MSC: 82C70 33E20 05C80 35R11 35R09 33C20 35R60 45K05 PDFBibTeX XMLCite \textit{J. C. Padrino}, Int. J. Appl. Comput. Math. 4, No. 5, Paper No. 131, 10 p. (2018; Zbl 1400.82252) Full Text: DOI
Ricciuti, Costantino; Toaldo, Bruno Semi-Markov models and motion in heterogeneous media. (English) Zbl 1386.82059 J. Stat. Phys. 169, No. 2, 340-361 (2017). MSC: 82C41 60K15 60K40 60G22 45E05 60G50 PDFBibTeX XMLCite \textit{C. Ricciuti} and \textit{B. Toaldo}, J. Stat. Phys. 169, No. 2, 340--361 (2017; Zbl 1386.82059) Full Text: DOI arXiv
Fa, Kwok Sau Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential. (English) Zbl 1343.60051 Ann. Phys. 353, 179-185 (2015). MSC: 60G50 60J60 35R11 35R09 45K05 92D20 PDFBibTeX XMLCite \textit{K. S. Fa}, Ann. Phys. 353, 179--185 (2015; Zbl 1343.60051) Full Text: DOI
Burch, Nathanial; Lehoucq, R. B. Computing the exit-time for a finite-range symmetric jump process. (English) Zbl 1330.35013 Monte Carlo Methods Appl. 21, No. 2, 139-152 (2015). MSC: 35A35 26A33 34A08 34B10 35A15 35L65 35B40 45A05 45K05 60G22 76R50 65C05 PDFBibTeX XMLCite \textit{N. Burch} and \textit{R. B. Lehoucq}, Monte Carlo Methods Appl. 21, No. 2, 139--152 (2015; Zbl 1330.35013) Full Text: DOI
Małolepszy, Tomasz Osgood type condition for the Volterra integral equations with bounded and nonincreasing kernels. (English) Zbl 1307.45002 J. Math. Anal. Appl. 410, No. 1, 411-417 (2014). MSC: 45D05 PDFBibTeX XMLCite \textit{T. Małolepszy}, J. Math. Anal. Appl. 410, No. 1, 411--417 (2014; Zbl 1307.45002) Full Text: DOI
Kadem, A.; Kirane, M.; Kirk, C. M.; Olmstead, W. E. Blowing-up solutions to systems of fractional differential and integral equations with exponential non-linearities. (English) Zbl 1333.35325 IMA J. Appl. Math. 79, No. 6, 1077-1088 (2014). MSC: 35R11 35B44 45D05 80A32 PDFBibTeX XMLCite \textit{A. Kadem} et al., IMA J. Appl. Math. 79, No. 6, 1077--1088 (2014; Zbl 1333.35325) Full Text: DOI
Thompson, Stephen; Seidman, Thomas I. Approximation of a semigroup model of anomalous diffusion in a bounded set. (English) Zbl 1275.47094 Evol. Equ. Control Theory 2, No. 1, 173-192 (2013). Reviewer: Hector O. Fattorini (Los Angeles) MSC: 47D06 60J35 60J75 45L05 58D25 35K57 92D30 PDFBibTeX XMLCite \textit{S. Thompson} and \textit{T. I. Seidman}, Evol. Equ. Control Theory 2, No. 1, 173--192 (2013; Zbl 1275.47094) Full Text: DOI
Pagnini, Gianni Erdélyi-Kober fractional diffusion. (English) Zbl 1276.26021 Fract. Calc. Appl. Anal. 15, No. 1, 117-127 (2012). MSC: 26A33 45D05 60G22 33E30 PDFBibTeX XMLCite \textit{G. Pagnini}, Fract. Calc. Appl. Anal. 15, No. 1, 117--127 (2012; Zbl 1276.26021) Full Text: DOI arXiv
Luchko, Yury Anomalous diffusion: models, their analysis, and interpretation. (English) Zbl 1279.60105 Rogosin, Sergei V. (ed.) et al., Advances in applied analysis. Selected papers based on the lectures presented at the 3rd international winter school “Modern Problems of Mathematics and Mechanics” held in Minsk, Belarus, January 2010. Basel: Birkhäuser (ISBN 978-3-0348-0416-5/hbk; 978-3-0348-0417-2/ebook). Trends in Mathematics, 115-145 (2012). MSC: 60J60 26A33 33E12 35B30 35B45 35B50 35K99 45K05 60J65 PDFBibTeX XMLCite \textit{Y. Luchko}, in: Advances in applied analysis. Selected papers based on the lectures presented at the 3rd international winter school ``Modern Problems of Mathematics and Mechanics'' held in Minsk, Belarus, January 2010. Basel: Birkhäuser. 115--145 (2012; Zbl 1279.60105) Full Text: DOI
Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun Analysis and approximation of nonlocal diffusion problems with volume constraints. (English) Zbl 1422.76168 SIAM Rev. 54, No. 4, 667-696 (2012). MSC: 76R50 45K05 76M10 26A33 35Q35 PDFBibTeX XMLCite \textit{Q. Du} et al., SIAM Rev. 54, No. 4, 667--696 (2012; Zbl 1422.76168) Full Text: DOI Link
Bandrowski, Bartosz; Karczewska, Anna; Rozmej, Piotr Numerical solutions to integral equations equivalent to differential equations with fractional time. (English) Zbl 1201.35020 Int. J. Appl. Math. Comput. Sci. 20, No. 2, 261-269 (2010). Reviewer: Titus Petrila (Cluj-Napoca) MSC: 35A35 45D05 65R20 35R09 35R11 PDFBibTeX XMLCite \textit{B. Bandrowski} et al., Int. J. Appl. Math. Comput. Sci. 20, No. 2, 261--269 (2010; Zbl 1201.35020) Full Text: DOI EuDML
Liu, F.; Yang, C.; Burrage, K. Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term. (English) Zbl 1170.65107 J. Comput. Appl. Math. 231, No. 1, 160-176 (2009). Reviewer: Hu Chuangan (San Jose) MSC: 65R20 26A33 60J70 45K05 45G10 PDFBibTeX XMLCite \textit{F. Liu} et al., J. Comput. Appl. Math. 231, No. 1, 160--176 (2009; Zbl 1170.65107) Full Text: DOI
Gorenflo, Rudolf; Mainardi, Francesco Some recent advances in theory and simulation of fractional diffusion processes. (English) Zbl 1166.45004 J. Comput. Appl. Math. 229, No. 2, 400-415 (2009). MSC: 45K05 26A33 60G18 60G50 60G51 60J60 PDFBibTeX XMLCite \textit{R. Gorenflo} and \textit{F. Mainardi}, J. Comput. Appl. Math. 229, No. 2, 400--415 (2009; Zbl 1166.45004) Full Text: DOI arXiv
Lv, Long-Jin; Xiao, Jian-Bin; Zhang, Lin; Gao, Lei Solutions for a generalized fractional anomalous diffusion equation. (English) Zbl 1158.45003 J. Comput. Appl. Math. 225, No. 1, 301-308 (2009). MSC: 45K05 26A33 76S05 PDFBibTeX XMLCite \textit{L.-J. Lv} et al., J. Comput. Appl. Math. 225, No. 1, 301--308 (2009; Zbl 1158.45003) Full Text: DOI arXiv
López-Fernández, María; Lubich, Christian; Schädle, Achim Adaptive, fast, and oblivious convolution in evolution equations with memory. (English) Zbl 1160.65356 SIAM J. Sci. Comput. 30, No. 2, 1015-1037 (2008). MSC: 65R20 45D05 44A10 65R10 PDFBibTeX XMLCite \textit{M. López-Fernández} et al., SIAM J. Sci. Comput. 30, No. 2, 1015--1037 (2008; Zbl 1160.65356) Full Text: DOI arXiv
Marseguerra, M.; Zoia, A. Monte Carlo evaluation of FADE approach to anomalous kinetics. (English) Zbl 1138.65003 Math. Comput. Simul. 77, No. 4, 345-357 (2008). MSC: 65C05 65C35 44A10 45K05 PDFBibTeX XMLCite \textit{M. Marseguerra} and \textit{A. Zoia}, Math. Comput. Simul. 77, No. 4, 345--357 (2008; Zbl 1138.65003) Full Text: DOI arXiv
Ervin, Vincent J.; Heuer, Norbert; Roop, John Paul Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation. (English) Zbl 1141.65089 SIAM J. Numer. Anal. 45, No. 2, 572-591 (2007). Reviewer: Ivan Secrieru (Chişinău) MSC: 65R20 45K05 65M60 35K55 65M15 45G10 26A33 PDFBibTeX XMLCite \textit{V. J. Ervin} et al., SIAM J. Numer. Anal. 45, No. 2, 572--591 (2007; Zbl 1141.65089) Full Text: DOI
Mainardi, Francesco; Pagnini, Gianni; Gorenflo, Rudolf Some aspects of fractional diffusion equations of single and distributed order. (English) Zbl 1122.26004 Appl. Math. Comput. 187, No. 1, 295-305 (2007). Reviewer: K. C. Gupta (Jaipur) MSC: 26A33 45K05 60G18 60J60 PDFBibTeX XMLCite \textit{F. Mainardi} et al., Appl. Math. Comput. 187, No. 1, 295--305 (2007; Zbl 1122.26004) Full Text: DOI arXiv
Andries, Erik; Umarov, Sabir; Steinberg, Stanly Monte Carlo random walk simulations based on distributed order differential equations with applications to cell biology. (English) Zbl 1132.65114 Fract. Calc. Appl. Anal. 9, No. 4, 351-369 (2006). MSC: 65R20 45K05 26A33 65C05 60G50 65L12 92C37 65L05 PDFBibTeX XMLCite \textit{E. Andries} et al., Fract. Calc. Appl. Anal. 9, No. 4, 351--369 (2006; Zbl 1132.65114) Full Text: arXiv EuDML
Duan, Junsheng; Chaolu, Temuer Scale-invariant solution for fractional anomalous diffusion equation. (English) Zbl 1093.45002 Ann. Differ. Equations 22, No. 1, 21-26 (2006). MSC: 45K05 26A33 33E30 PDFBibTeX XMLCite \textit{J. Duan} and \textit{T. Chaolu}, Ann. Differ. Equations 22, No. 1, 21--26 (2006; Zbl 1093.45002)
Schädle, Achim; López-Fernández, María; Lubich, Christian Fast and oblivious convolution quadrature. (English) Zbl 1111.65114 SIAM J. Sci. Comput. 28, No. 2, 421-438 (2006). MSC: 65R20 45D05 45E10 45G10 45J05 PDFBibTeX XMLCite \textit{A. Schädle} et al., SIAM J. Sci. Comput. 28, No. 2, 421--438 (2006; Zbl 1111.65114) Full Text: DOI arXiv
Cuesta, Eduardo; Lubich, Christian; Palencia, Cesar Convolution quadrature time discretization of fractional diffusion-wave equations. (English) Zbl 1090.65147 Math. Comput. 75, No. 254, 673-696 (2006). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65R20 26A33 45K05 45G10 PDFBibTeX XMLCite \textit{E. Cuesta} et al., Math. Comput. 75, No. 254, 673--696 (2006; Zbl 1090.65147) Full Text: DOI
Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.; Gonchar, V. Yu. Distributed order time fractional diffusion equation. (English) Zbl 1089.60046 Fract. Calc. Appl. Anal. 6, No. 3, 259-279 (2003). Reviewer: Rudolf Gorenflo (Berlin) MSC: 60J60 26A33 45K05 82C31 PDFBibTeX XMLCite \textit{A. V. Chechkin} et al., Fract. Calc. Appl. Anal. 6, No. 3, 259--279 (2003; Zbl 1089.60046)
Duan, Junsheng; Xu, Mingyu Concentration distribution of fractional anomalous diffusion caused by an instantaneous point source. (English) Zbl 1145.76432 Appl. Math. Mech., Engl. Ed. 24, No. 11, 1302-1308 (2003). MSC: 76R50 35R99 26A33 45K05 33E20 PDFBibTeX XMLCite \textit{J. Duan} and \textit{M. Xu}, Appl. Math. Mech., Engl. Ed. 24, No. 11, 1302--1308 (2003; Zbl 1145.76432) Full Text: DOI
Hanyga, Andrzej Multi-dimensional solutions of space-time-fractional diffusion equations. (English) Zbl 0999.60035 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2018, 429-450 (2002). Reviewer: Rudolf Gorenflo (Berlin) MSC: 60G18 60J60 45K05 PDFBibTeX XMLCite \textit{A. Hanyga}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2018, 429--450 (2002; Zbl 0999.60035) Full Text: DOI
Biler, Piotr; Woyczyński, Wojbor A. Nonlocal quadratic evolution problems. (English) Zbl 0953.35070 Bojarski, Bogdan (ed.) et al., Evolution equations. Existence, regularity and singularities. Proceedings of the minisemester, Warsaw, Poland, September 21-October 2, 1998. Warsaw: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 52, 11-24 (2000). MSC: 35K60 35B40 45K05 82C21 PDFBibTeX XMLCite \textit{P. Biler} and \textit{W. A. Woyczyński}, Banach Cent. Publ. 52, 11--24 (2000; Zbl 0953.35070) Full Text: EuDML
Baumann, G.; Südland, N.; Nonnenmacher, T. F. Anomalous relaxation and diffusion processes in complex systems. (English) Zbl 0972.82080 Transp. Theory Stat. Phys. 29, No. 1-2, 157-171 (2000). MSC: 82C70 45K05 60K20 26A33 PDFBibTeX XMLCite \textit{G. Baumann} et al., Transp. Theory Stat. Phys. 29, No. 1--2, 157--171 (2000; Zbl 0972.82080) Full Text: DOI