[1] D. A. Benson, R. Schumer, M. M. Meerschaert, and S. W. Wheatcraft, Fractional dispersion, Levy motion, and the MADE tracer tests, Transport in porous media, 42 (2001), 211-240.
[2] B. OShaughnessy and I. Procaccia, Analytical solutions for diffusion on fractal objects, Physical review letters, 54 (1985), 455.
[3] M. R. Ubriaco, A simple mathematical model for anomalous diffusion via Fisher’s information theory, Physics Letters, 373 (2009), 4017-4021.
[4] M. Fardi, A kernel-based pseudo-spectral method for multi-term and distributed order time-fractional diffusion equations, Numerical Methods Partial Differential Equations, 39(2023), 2630-2651.
[5] M. Fardi, S.-K.-Q. Al-Omari, and S. Araci, S. A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation, Advance in Continuous Discrete Models, 54 (2022), 1-14.
[6] M. Fardi, M. A. Zaky, and A. S. Hendy, Nonuniform difference schemes for multi-term and distributed-order fractional parabolic equations with fractional Laplacian, Mathematic and Computers in Simulation, 206 (2023), 614–635.
[7] M. Fardi, Y. Khan, A fast difference scheme on a graded mesh for time-fractional and space distributedorder diffusion equation with nonsmooth data, International Journall of Modern Physics B, 36 (2022), 2250076.
[8] M. Fardi, and M. Ghasemi, A numerical solution strategy based on error analysis for time-fractional mobile/immobile transport model, Soft Computing, 25 (2021), 11307–11331.
[9] S. Mohammadi, M. Ghasemi, and M. Fardi, A fast Fourier spectral exponential time-differencing method for solving the time- fractional mobile-immobile advection-dispersion equation, Computational and Applied Mathematics, 41 (2022), 264.
[10] M. Fardi and E. Amini, Numerical investigation of a new difference scheme on a graded mesh for solving the time-space fractional sub-diffusion equations with nonsmooth solutions, Journal of Advanced Mathematical Modeling, 12 (2022), 212-231.
[11] E. Amini, Optimal Control Problems: Convergence and Error Analysis in Reproducing Kernel Hilbert Spaces, Control and Optimization in Applied Mathematics, 6 (2021), 53-77.
[12] Z. Hao and W. Cao, An improved algorithm based on finite difference schemes for fractional boundary value problems with nonsmooth solution, Journal of Scientific Computing, 73 (2017), 395-415.
[13] M. M. Meerschaert and C. Tadjeran, Finite difference approximations for fractional advectiondispersion flow equations, Journal of computational and applied mathematics, 172 (2004), 65-77.
[14] Z. Zhao, Y. Zheng , and P. Guo, A Galerkin finite element method for a class of time-space fractional differential equation with nonsmooth data, Journal of Scientific Computing, 70 (2017), 386-406.
[15] Z. Hao, M. Park, G. Lin and Z. Cai, Finite element method for two-sided fractional differential equations with variable coefficients: Galerkin approach, Journal of Scientific Computing, 79 (2019), 700-717.
[16] F. Zeng, Z. Mao, and G. E. Karniadakis, A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities, SIAM Journal on Scientific Computing, 39(2017), A360-A383.
[17] Z. Zhang, F. Zeng, and G. E. Karniadakis, Optimal error estimates of spectral Petrov-Galerkin and collocation methods for initial value problems of fractional differential equations, SIAM Journal on Numerical Analysis, 53 (2015), 2074-2096.
[18] Q. Xu and J. S. Hesthaven, Discontinuous Galerkin method for fractional convection-diffusion equations, SIAM Journal on Numerical Analysis, 52(2014), 405-423.
[19] A. Simmons, Q. Yang, and T. Moroney, A finite volume method for two-sided fractional diffusion equations on non-uniform meshes, Journal of Computational Physics, 335 (2017), 747-759.
[20] M. Caputo, and M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl, 1 (2015), 1-13.
[21] J. Losada, and J. J. Nieto, Properties of a new fractional derivative without singular kernel, Progr. Fract. Differ. Appl, 1 (2015), 87-92.
[22] M. Caputo, and M. Fabrizio, Applications of new time and spatial fractional derivatives with exponential kernels, Progr. Fract. Differ. Appl, 2 (2016), 1-11.
[23] M. A. Dokuyucu, E. Celik, H. Bulut, and H. M. Baskonus, Cancer treatment model with the Caputo-Fabrizio fractional derivative, The European Physical Journal Plus, 133(2018), 1-6.
[24] S. Bushnaq, S. A. Khan, K. Shah, and G. Zaman, Mathematical analysis of HIV/AIDS infection model with Caputo-Fabrizio fractional derivative, Cogent Mathematics & Statistics, 5 (2018), 1432521.
[25] D. Baleanu, A. Jajarmi, H. Mohammadi, and S. Rezapour, A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative, Chaos, Solitons & Fractals, 134 (2020), 109705.
[26] L. Zhengguang, A. Cheng, and L. Xiaoli, A second-order finite difference scheme for quasilinear time fractional parabolic equation based on new fractional derivative, International Journal of Computer Mathematics, 95 (2018), 396-411.
[27] J. Shen, T. Tang, and L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer, 2013.
[28] C. Canuto, and A. Quarteroni, Approximation results for orthogonal polynomials in Sobolev spaces, Mathematics of Computation, 38 (1982), 67-86.
[29] A. Quarteroni and A. Valli, Numerical approximation of partial differential equations, Springer Science & Business Media, 2008.
[30] C. Bernardi and Y. Maday, Approximations spectrales de problemes aux limites elliptiques, Springer, 1992.
)