[
[1] I.M. Sokolov, J. Klafter and A. Blumen, Fractional kinetics, Physics Today, 55 (2002), 48–54.10.1063/1.1535007
]Search in Google Scholar
[
[2] R. Hilfer, Applications of Fractional Calculus in Physics, Word Scientific, Singapore, (2000).10.1142/3779
]Search in Google Scholar
[
[3] B. Baeumer, D.A. Benson, M.M. Meerschaert and S.W. Wheatcraft, Subordinated advection-dispersion equation for contaminant transport, Water Resources Research, 37 (2001), 1543–1550.10.1029/2000WR900409
]Search in Google Scholar
[
[4] D.A. Benson, S.W. Wheatcraft and M.M. Meerschaert, Application of a fractional advection-dispersion equation, Water resources research, 36 (2000), 1403–1412.10.1029/2000WR900031
]Search in Google Scholar
[
[5] D.A. Benson, R. Schumer, M.M. Meerschaert and S.W. Wheatcraft, Fractional dispersion, Lévy motion, and the MADE tracer tests, Transport in porous media, 42 (2001), 211–240.10.1023/A:1006733002131
]Search in Google Scholar
[
[6] R. Schumer, D.A. Benson, M.M. Meerschaert and S.W. Wheatcraft, Eulerian derivation of the fractional advection–dispersion equation, Journal of contaminant hydrology, 48 (2001), 69–88.10.1016/S0169-7722(00)00170-4
]Search in Google Scholar
[
[7] R.L. Magin, Fractional calculus in bioengineering, part 1, Critical Reviews in Biomedical Engineering, 32 (2004).10.1615/CritRevBiomedEng.v32.10
]Search in Google Scholar
[
[8] F. Mainardi, M. Raberto, R. Gorenflo and E. Scalas, Fractional calculus and continuous-time finance II: the waiting-time distribution, Physica A: Statistical Mechanics and its Applications, 287 (2000), 468–481.10.1016/S0378-4371(00)00386-1
]Search in Google Scholar
[
[9] L. Sabatelli, S. Keating, J. Dudley and P. Richmond, Waiting time distributions in financial markets, The European Physical Journal B-Condensed Matter and Complex Systems, 27 (2002), 273–275.
]Search in Google Scholar
[
[10] E. Scalas, R. Gorenflo and F. Mainardi, Fractional calculus and continuous-time finance, Physica A: Statistical Mechanics and its Applications, 284 (2000), 376–384.10.1016/S0378-4371(00)00255-7
]Search in Google Scholar
[
[11] R. Gorenflo, F. Mainardi, E. Scalas and M. Raberto, Fractional calculus and continuous-time finance III: the diffusion limit, Mathematical finance, (2001), 171–180.10.1007/978-3-0348-8291-0_17
]Search in Google Scholar
[
[12] S. Dipierro, B. Pellacci, E. Valdinoci and G. Verzini, Time-fractional equations with reaction terms: Fundamental solutions and asymptotics, Discrete & Continuous Dynamical Systems-A, (2020).
]Search in Google Scholar
[
[13] F. Mainardi, On some properties of the Mittag-Leffler function Eα(-tα), completely monotone for t > 0 with 0 < α < 1, Discrete & Continuous Dynamical Systems-B, 19 (2014), 1267–2278.10.3934/dcdsb.2014.19.2267
]Search in Google Scholar
[
[14] W. Chen, C. Li and J. Zhu, Fractional equations with indefinite nonlinearities, Discrete & Continuous Dynamical Systems-A, 39 (2019), 1257–1268.10.3934/dcds.2019054
]Search in Google Scholar
[
[15] M.AL Horani, M. Fabrizio, A. Favini and H. Tanabe, Fractional Cauchy problems and applications, Discrete & Continuous Dynamical Systems-S, 13 (2020), 2259-2270.10.3934/dcdss.2020187
]Search in Google Scholar
[
[16] P. Agarwal and A.A. El-Sayed, Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation, Physica A: Statistical Mechanics and Its Applications, 500 (2018), 40–49.10.1016/j.physa.2018.02.014
]Search in Google Scholar
[
[17] H.U. Molla and M.H. Nova, Lagranges Spectral Collocation Method for Numerical Approximations of Two-Dimensional Space Fractional Diffusion Equation, American Journal of Computational Mathematics, 8 (2018), 720–726.10.4236/ajcm.2018.82010
]Search in Google Scholar
[
[18] Y.N. Zhang and Z.Z. Sun, Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation, Journal of Computational Physics, 230 (2011), 8713–8728.10.1016/j.jcp.2011.08.020
]Search in Google Scholar
[
[19] Q. Yang, I. Turner, F. Liu and M. Ilić, Novel numerical methods for solving the time-space fractional diffusion equation in two dimensions, SIAM Journal on Scientific Computing, 33 (2011), 1159–1180.10.1137/100800634
]Search in Google Scholar
[
[20] F. Liu, P. Zhuang, I. Turner, K. Burrage and V. Anh, A new fractional finite volume method for solving the fractional diffusion equation, Applied Mathematical Modelling, 38 (2014), 3871–3878.10.1016/j.apm.2013.10.007
]Search in Google Scholar
[
[21] M.M. Meerschaert, H.P. Scheffler and C. Tadjeran,Finite difference methods for two-dimensional fractional dispersion equation, Journal of Computational Physics, 211 (2006), 249–261.10.1016/j.jcp.2005.05.017
]Search in Google Scholar
[
[22] S. Jaiswal, M. Chopra and S. Das, Numerical solution of non-linear partial differential equation for porous media using operational matrices, Mathematics and Computers in Simulation, 160 (2019), 138–154.10.1016/j.matcom.2018.12.007
]Search in Google Scholar
[
[23] AH Bhrawy, E.H. Doha, D. Baleanu and S.S. Ezz-Eldien, A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations, Journal of Computational Physics, 293 (2015), 142–156.10.1016/j.jcp.2014.03.039
]Search in Google Scholar
[
[24] E.H. Doha, A.H. Bhrawy and S.S. Ezz-Eldien, A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order, Computers & Mathematics with Applications, 62 (2011), 2364–2373.10.1016/j.camwa.2011.07.024
]Search in Google Scholar
[
[25] M. Dehghan, S.A. Yousefi and A. Lotfi, The use of He’s variational iteration method for solving the telegraph and fractional telegraph equations, International Journal for Numerical Methods in Biomedical Engineering, 27 (2011),219–231.10.1002/cnm.1293
]Search in Google Scholar
[
[26] A. Singh, M. Chopra and S. Das, Study and analysis of a two-dimensional nonconservative fractional order aerosol transport equation, Mathematical Methods in the Applied Sciences, 42 (2019), 2939–2948.10.1002/mma.5524
]Search in Google Scholar
[
[27] A. Saadatmandi and M. Dehghan, A new operational matrix for solving fractional-order differential equations, Computers & mathematics with applications, 59 (2010), 1326–1336.10.1016/j.camwa.2009.07.006
]Search in Google Scholar
[
[28] W.M. Abd-Elhameed and Y.H. Youssri, Spectral solutions for fractional differential equations via a novel Lucas operational matrix of fractional derivatives, Rom. J. Phys, 61 (2016), 795–813.
]Search in Google Scholar
[
[29] E. Tohidi, A.H. Bhrawy and Kh. Erfani, A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation, Applied Mathematical Modelling, 37 (2013), 4283–4294.10.1016/j.apm.2012.09.032
]Search in Google Scholar
[
[30] S. Das, Analytical solution of a fractional diffusion equation by variational iteration method, Computers & Mathematics with Applications, 57 (2009), 483–487.10.1016/j.camwa.2008.09.045
]Search in Google Scholar
[
[31] S. Das, P.K. Gupta and P. Ghosh, An approximate solution of nonlinear fractional reaction–diffusion equation, Applied mathematical modelling, 35 (2011), 4071–4076.10.1016/j.apm.2011.02.004
]Search in Google Scholar
[
[32] K. Vishal, S. Kumar and S. Das, Application of homotopy analysis method for fractional Swift Hohenberg equation–revisited, Applied Mathematical Modelling, 36 (2012), 3630–3637.10.1016/j.apm.2011.10.001
]Search in Google Scholar
[
[33] S. Kumar, P. Pandey, S. Das and E.M. Craciun, Numerical solution of two dimensional reaction–diffusion equation using operational matrix method based on Genocchi polynomial. Part I: Genocchi polynomial and operational matrix, Proc. Rom. Acad., Ser. A: Math. Phys. Tech. Sci. Inf. Sci., 20 (2019), 393–399.
]Search in Google Scholar
