R. Klages, G. Radons, I.M. Sokolov (Editors), Anomalous Transport: Foundations and Applications, in Nonlinear and Complex Systems (Wiley-VCH, 2008)
J. Liu, H. Li, Y. Liu, J. Appl. Math. Comput. 52, 345 (2016)
I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, Calif, 1999)
R. Hilfer (Editor), Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000)
A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, North-Holland Math. Stud. 204, 1 (2006)
R.L. Magin, O. Abdullah, D. Baleanu, X.J. Zhou, J. Magn. Reson. 190, 255 (2008)
D. Baleanu, Phys. Scr. 2009, 014006 (2009)
M. Caputo, M. Fabrizio, Prog. Fract. Differ. Appl. 1, 73 (2015)
A. Atangana, D. Baleanu, Therm. Sci. 20, 763 (2016)
D. Baleanu, A. Jajarmi, E. Bonyah, M. Hajipour, Adv. Differ. Equ. 2018, 230 (2018)
A. Atangana, I. Koca, Chaos, Solitons Fractals 89, 447 (2016)
A. Atangana, Physica A 505, 688 (2018)
A. Atangana, J. Gómez-Aguilar, Eur. Phys. J. Plus 133, 166 (2018)
B.S.T. Alkahtani, A. Atangana, I. Koca, J. Nonlinear Sci. Appl. 10, 3191 (2017)
X.-J. Yang, H.M. Srivastava, J.A. Tenreiro Machado, Therm. Sci. 20, 753 (2016)
A.-M. Yang, Y. Han, J. Li, W.-X. Liu, Therm. Sci. 20, 717 (2016)
B. Saad, T. Alkahtania, I. Kocab, A. Atangana, J. Nonlinear Sci. Appl. 10, 4231 (2017)
X.-J. Yang, J.A. Tenreiro Machado, J.J. Nieto, Fund. Inform. 151, 63 (2017)
T.A.M. Langlans, B. Henry, S. Wearne, SIAM J. Appl. Math. 71, 1168 (2011)
B. Henry, T.A.M. Langlands, S.L. Wearne, Phys. Rev. Lett. 100, 128103 (2008)
F. Liu, Q. Yang, I. Turner, J. Comput. Nonlinear Dyn. 6, 011009 (2011)
X. Hu, L. Zhang, Appl. Math. Model. 36, 4027 (2012)
A.T. Balasim, N.H.M. Ali, AIP Conf. Proc. 1870, 040050 (2017)
A.H. Bhrawy, M.A. Zaky, Nonlinear Dyn. 80, 101 (2015)
B. Yu, X. Jiang, J. Sci. Comput. 68, 252 (2016)
H. Zhang, X. Yang, X. Han, Comput. Math. Appl. 68, 1710 (2014)
M. Cui, J. Comput. Phys. 228, 7792 (2009)
J.W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods (Springer, 1998)
R. Du, W.R. Cao, Z.Z. Sun, Appl. Math. Model. 34, 2998 (2010)
J.A. Abraham, G. Gilberto, M. Benito, Math. Comput. Simul. 121, 48 (2016)
A.J. Arenas, G. González-Parra, B.M. Caraballo, Math. Comput. Model. 57, 1663 (2013)
H.A. Obaid, R. Ouifki, K.C. Patidar, Int. J. Appl. Math. Comput. Sci. 23, 357 (2013)
R.E. Mickens, J. Differ. Equ. Appl. 8, 823 (2002)
R.E. Mickens, Applications of Nonstandard Finite Difference Schemes (World Scientifc, 2000)
M. Díaz-Rodríguez, G. González-Parra, A.J. Arenas, Int. J. Numer. Methods Biomed. Eng. 27, 1211 (2011)
R.E. Mickens, Methods Part. Differ. Equ. Fractals 15, 201 (1999)
G. González-Parra, A.J. Arenas, B.M. Chen-Charpentier, Math. Comput. Model. 54, 1030 (2010)
N.H. Sweilam, S.M. AL-Mekhlafi, J. Adv. Res. 7, 271 (2016)
K.B. Oldham, J. Spanier, The Fractional Calculus (Academic Press, New York, NY, USA, 1974)
B.P. Demidovich, I.A. Maron, Computational Mathematics (Mir Publishers, Moscow, 1987)
G.D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, second ed. (Oxford University Press, 1978)
R.D. Richtmyer, K.W. Morton, Difference Methods for Initial-Value Problems (InterScience Publishers, John Wiley, New York, 1967)
S.B. Yuste, L. Acedo, SIAM J. Numer. Anal. 42, 1862 (2005)
N.H. Sweilam, M.M. Abou Hasan, Eur. Phys. J. Plus 132, 212 (2017)
N.H. Sweilam, S.M. AL-Mekhlafi, D. Baleanu, J. Adv. Res. 17, 125 (2019)
