Page 175 - IJOCTA-15-3
P. 175
A numerical method for solving distributed-order multi-term time-fractional telegraph equations involving
24. Mainardi F, Pagnini G. The role of the 36. Abbaszadeh M, Dehghan M. Meshless upwind
Fox-Wright functions in fractional sub-diffusion local radial basis function-finite difference tech-
of distributed order. J Comput Appl Math. nique to simulate the time-fractional distributed-
2007;207(2):245-257. order advection-diffusion equation. Eng Comput.
https://doi.org/10.1016/j.cam.2006.10.014 2021;37:873-889.
25. Ahmed HF, Moubarak MRA, Hashem WA. https://doi.org/10.1007/s00366-019-00861-7
Gegenbauer spectral tau algorithm for solving 37. Ye H, Liu F, Anh V. Compact difference scheme
fractional telegraph equation with convergence for distributed-order time-fractional diffusion-
analysis. Pramana - J Phys. 2021;95(2):1-16. wave equation on bounded domains. J Comput
https://doi.org/10.1007/s12043-021-02113-0 Phys. 2015;298:652-660.
26. Zhang Y, Qian J, Papelis C, Sun P, Yu Z. Im- https://doi.org/10.1016/j.jcp.2015.06.025
˜
proved understanding of bimolecular reactions 38. Chen H, LA¼ S, Chen W. Finite differ-
in deceptively simple homogeneous media: from ence/spectral approximations for the distributed
laboratory experiments to Lagrangian quantifica- order time fractional reaction-diffusion equation
tion. Water Resour Res. 2014;50(2):1704-1715. on an unbounded domain. J Comput Phys.
https://doi.org/10.1002/2013WR014711 2016;315:84-97.
27. Sun HG, Chen W, Li C, Chen YQ. Fractional dif- https://doi.org/10.1016/j.jcp.2016.03.044
ferential models for anomalous diffusion. Physica 39. Qiu W, Xu D, Chen H, Guo J. An alternating
A: Stat Mech Appl. 2010;389(14):2719-2724. direction implicit Galerkin finite element method
https://doi.org/10.1016/j.physa.2010.02.030 for the distributed-order time-fractional mobile-
28. Gao GH, Sun ZZ. Two difference schemes for solv- immobile equation in two dimensions. Comput
ing the one-dimensional time distributed-order Math Appl. 2020;80(12):3156-3172.
fractional wave equations. Numer Algorithms. https://doi.org/10.1016/j.camwa.2020.11.003
2017;74:675-697. 40. Yang Z, Zheng X, Wang H. A variably
https://doi.org/10.1007/s11075-016-0167-y distributed-order time-fractional diffusion equa-
29. Wang Z, Vong S. Compact difference schemes for tion: analysis and approximation. Comput Meth-
the modified anomalous fractional sub-diffusion ods Appl Mech Eng. 2020;367:113118.
equation and the fractional diffusion-wave equa- https://doi.org/10.1016/j.cma.2020.113118
tion. J Comput Phys. 2014;277:1-15. 41. Abdelkawy MA, Lopes AM, Zaky MA. Shifted
https://doi.org/10.1016/j.jcp.2014.08.012 fractional Jacobi spectral algorithm for solving
30. Ye H, Liu F, Anh V, Turner I. Numerical analy- distributed order time-fractional reaction-
sis for the time distributed-order and Riesz space diffusion equations. Comput Appl Math.
fractional diffusions on bounded domains. IMA J 2019;38:1-21.
Appl Math. 2015;80(3):825-838. https://doi.org/10.1007/s40314-019-0845-1
https://doi.org/10.1093/imamat/hxu015 42. Ansari A, Derakhshan MH. On spectral po-
31. Jian HY, Huang TZ, Gu XM, Zhao YL. Fast lar fractional Laplacian. Math Comput Simul.
second-order implicit difference schemes for time 2023;206:636-663.
distributed–order and Riesz X.L. space fractional https://doi.org/10.1016/j.matcom.2022.12.008
diffusion–wave equations. Comput Math Appl. 43. Derakhshan MH, Aminataei A. A numerical
2021;94:136-154. method for finding solution of the distributed-
https://doi.org/10.1016/j.camwa.2021.05.003 order time-fractional forced Kortewegde Vries
32. Kharazmi E, Zayernouri M, Karniadakis G. equation including the Caputo fractional deriv-
Petrov-Galerkin and spectral collocation methods ative. Math Methods Appl Sci. 2022;45(5):3144-
for distributed order differential equations. SIAM 3165.
J Sci Comput. 2017;39:A1003-A1037. https://doi.org/10.1002/mma.7981
https://doi.org/10.1137/16M1073121 44. Ahmed HF, Hashem WA. Improved Gegen-
33. Gao G, Sun Z. Two alternating direction implicit bauer spectral tau algorithms for distributed-
difference schemes with the extrapolation method order time-fractional telegraph models in multi-
for the two-dimensional distributed-order differ- dimensions. Numer Algorithms. 2023; 93(3):1013-
ential equations. Comput Math Appl. 2015;69: 1043.
926-948. https://doi.org/10.1007/s11075-022-01452-2
https://doi.org/10.1016/j.camwa.2015.02.023 45. Ilic M, Liu F, Turner I, Anh V. Numerical approx-
34. Duong P, Kwok E, Lee M. Deterministic analy- imation of a fractional-in-space diffusion equa-
sis of distributed order systems using operational tion, I. Fract Calc Appl Anal. 2005;8(3):323-341.
matrix. Appl Math Model. 2016;40:1929-1940. http://eudml.org/doc/11303
https://doi.org/10.1016/j.apm.2015.09.035 46. Morgado ML, Rebelo M. Numerical approxima-
35. Mashayekhi S, Razzaghi M. Numerical solu- tion of distributed order reaction-diffusion equa-
tion of distributed order fractional differential tions. J Appl Math Comput. 2015; 275:216-227.
equations by hybrid functions. J Comput Phys. https://doi.org/10.1016/j.cam.2014.07.029
2016;315:169-181. 47. Moghaddam BP, Tenreiro Machado JA, Morgado
https://doi.org/10.1016/j.jcp.2016.01.041 ML. Numerical approach for a class of distributed
547

