[1] J. Cheng, J. Nakagawa, M. Yamamoto and T. Yamazaki, Uniqueness in an inverse problem for a one dimensional fractional diffusion equation, Inv. Prob. 25 (2009) 115002.
[2] M.D. Echeverry and C.E. Mejía , A two dimensional discrete mollification operator and the numerical solution of an inverse source problem, AXIOMS 7(4), 89 (2018).
[3] A. Fahim, M.A. Fariborzi Araghi, J. Rashidinia and M. Jalalvand, Numerical solution of Volterra partial integro-differential equations based on Sinc-collocation method, Advances in Difference Equations 362 (2017) 1–21. DOI 10.1186/s13662-017-1416 7.
[4] M. Garshasbi and H. Dastour, Estimation of unknown boundary functions in an inverse heat conduction problem using a mollified marching scheme, Numer. Algor. 68 (2015) 769–790.
[5] M. Garshasbi and H. Dastour, A mollified marching solution of an inverse ablation-type moving boundary problem, Comput. Appl. Math. 35 ( 2016) 60–73.
[6] M. Garshasbi, P. Reihani and H. Dastour, A stable numerical solution of a class of semi-linear Cauchy problems, J. Adv. Res. Dyn. Cont. Sys. 4 (2012) 56–67.
[7] R. Yan, M. Han, Q. Ma and X. Ding, A spectral collocation method for nonlinear fractional initial value problems with a variable-order fractional derivative, Comput. Appl. Math. 38, 66 (2019) 1–25.
[8] M. Jalalvand, B. Jazbi and M.R. Mokhtarzadeh, A finite difference method for the smooth solution of linear Volterra integral equations, Int. J. Non-linear Anal. Appl. 4(2) (2013) 1–10.
[9] Y. Lin and C. Xu, Finite difference-spectral approximation for the time-fractional diffusion equation, J. Comp. Phys. 225 (2007) 1533-1552.
[10] Y. Luchko, Maximum principle and its application for the time-fractional diffusion equations, Fract. Calcul. and Appl. Anal., 14 (2011) 110-124.
[11] A. Kumar, A moving boundary problem with space-fractional diffusion logistic population model and density-dependent dispersal rate, Appl. Math. Model. 88 (2020) 51-65.
[12] C.E. Mejía and A. Piedrahita, Solution of a time fractional inverse advection-dispersion problem by discrete mollification, Rev. Colomb. Mat. 51 (2017) 83–102.
[13] C.E. Mejía and A. Piedrahita, finite difference approximation of a two dimensional time fractional advection-dispersion problem, arXiv (2018), arXiv:1807.07393v1.
[14] R. Metzler and J. Klafter, The random walks guide to anomalous diffusion: a fractional dynamics approach, Physics Reports, Volume 339, Issue 1, (2000) 1-77.
[15] D.A. Murio, Mollification and Space Marching, in: K.Woodbury (Ed.), Inverse Engineering Handbook, CRC Press, Boca Raton, Florida, (2002).
[16] D.A. Murio, On the stable numerical evaluation of Caputo fractional derivatives, Comput. Math. Appl. 51 (2006) 1539-1550.
[17] R.R. Nigmatullin, The realization of the generalized transfer equation in a medium with fractal geometry, Phys. Stat. Sol. B 133 (1986) 25-30.
[18] M.A. Zaky, An accurate spectral collocation method for nonlinear systems of fractional differential equations and related integral equations with nonsmooth solutions, Appl. Numer. Math. 154 (2020) 205-222.
[19] C. Milici, G. Drăgănescu and J. T. Machado, Introduction to fractional differential equations, Springer, (2019).
[20] K. Sakamoto and M. Yamamoto, Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems, preprint UTMS (2010) 2010–2014.
[21] Z.Z. Sun and X.N. Wu, A full discrete difference scheme for a diffusion-wave system, Appl. Numer. Math. 56 (2006) 193–209.
[22] T. Wei and Z.Q. Zhang, Reconstruction of a time-dependent source term in a time-fractional diffusion equation, Eng Anal Bound Elem 37 (2013), 23–31.
[23] Y. Zhang and X. Xu, Inverse source problem for a fractional diffusion equation, Inv. Prob. 27 (2011) 035010.
[24] L. Zhou and H.M. Selim, Application of the fractional advection-dispersion equations in porous media, Soil Sci. Soc. Am. J. 64 (4) (2003) 1079–1084.