- [1] S. Abbasbandy, S. Kazem, M. S. Alhuthali, and H. H. Alsulami, Application of the operational matrix of fractional order Legendre functions for solving the time-fractional convectiondiffusion equation, Appl. Math. Comput., 266 (2015), 31–40.
- [2] I. G. Ameen, M. A. Zaky, and E. H. Doha, Singularity preserving spectral collocation method for nonlinear systems of fractional differential equations with the right-sided Caputo fractional derivative, Math. Comput. Simul., 392 (2021).
- [3] A. Baseri, S. Abbasbandy, and E. Babolian, A collocation method for fractional diffusion equation in a long time with Chebyshev functions, Appl. Math. Comput., 322 (2018), 55–65.
- [4] L. Beghin and C. Ricciuti, Lvy Processes Linked to the Lower-Incomplete Gamma Function, Fractal. Fract., 5 (2021).
- [5] H. Chen, S. Lu¨, and W. Chen, Spectral methods for the time fractional diffusion-wave equation in a semi-infinite channel, Comput. Math. Appl., 71 (2016), 1818–1830.
- [6] M. Dehghan, M. Abbaszadeh, and A. Mohebbi, Error estimate for the numerical solution of fractional reactionsub-diffusion process based on a meshless method, J. Comput. Appl. Math., 280 (2015), 14–36.
- [7] M. D’Elia, C. Glusa, T. Abdeljawad, and N. Mlaiki, A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems, Numer. Methods. Partial. Differ. Equ., 38 (2022), 2084–2103.
- [8] C. S. Drapaca, The Impact of Anomalous Diffusion on Action Potentials in Myelinated Neurons, Fractal Fract., 5 (2021).
- [9] 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, Comput. Math. appl., 62 (2011), 2364–2373.
- [10] H. Hassani and Z. Avazzadeh, Novel operational matrices for solving 2-dim nonlinear variable order fractional optimal control problems via a new set of basis functions, Appl. Numer. Math., 166 (2021), 26–39.
- [11] M. R. Hooshmandasl, M. H. Heydari, and C. Cattani, Numerical solution of fractional sub-diffusion and timefractional diffusion-wave equations via fractional-order Legendre functions, Eur. Phys. J. Plus., 131 (2016).
- [12] M. Jani, E. Babolian and B. Dambaru, A Petrov-Galerkin spectral method for the numerical simulation and analysis of fractional anomalous diffusion, Int. J. Comput. Math., 44 (2020), 2021–2032.
- [13] F. Kamali and H. Saeedi, Generalized fractional-order Jacobi functions for solving a nonlinear systems of fractional partial differential equations numerically, Math. Methods Appl. Sci., 41 (2017), 3155–3174.
- [14] F. Lin and H. Qu, A Runge-Kutta Gegenbauer spectral method for nonlinear fractional differential equations with Riesz fractional derivatives, Int. J. Comput. Math., 96 (2018), 417–435.
- [15] N. Mendes, M. Chhay, J. Berger, and D. Dutykh, Numerical Methods for Diffusion Phenomena in Building Physics, Springer Cham, 2019.
- [16] M. Molavi-Arabshahi, J. Rashidinia, and S. Tanoomand, An efficient spectral collocation method based on the generalized Laguerre polynomials to multi-term time fractional diffusion-wave equations, AIP Advances, 14(2) (2024), DOI: 10.1063/5.0187493.
- [17] M. Molavi-Arabshahi, J. Rashidinia, and M. Yousefi, An efficient approach for solving the fractional model of the human T-cell lymphotropic virus I by the spectral method, Journal of Mathematical Modeling, 11(3) (2023), 463–477.
- [18] N. Rajagopala, S. Balajia, R. Seethalakshmia, and V. S. Balajib, A new numerical method for fractional order Volterra integro-differential equations, Ain. Shams. Eng. J., 11 (2020), 171–177.
- [19] J. Rashidinia, T. Eftekhari, and K. Maleknejad, Numerical solutions of two-dimensional nonlinear fractional Volterra and Fredholm integral equations using shifted Jacobi operational matrices via collocation method, J. King. Saud. Univ. Sci., 33 (2021).
- [20] J. Rashidinia and E. Mohmedi, Approximate solution of the multi-term time fractional diffusion and diffusionwave equations, Comp. Appl. Math., 39 (2020).
- [21] J. Shen, T. Tang, and L. Wang, Spectral methods, Algorithms, analysis and applications, Springer, 2010.
- [22] N. H. Sweilam, S. M. Ahmed, and M. Adel, A simple numerical method for two-dimensional nonlinear fractional anomalous sub-diffusion equations, Math. Method. Appl. Sci., 5 (2020), 2914–2933.
- [23] I. Talib, F. Jarad, M. U. Mirza, A. Nawaz, and M. B. Riaz, A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations, Alex. Eng. J., 61 (2013), 135–145.
- [24] L. Z. Wu, S. R. Zhu, and J. Peng, Application of the Chebyshev spectral method to the simulation of groundwater flow and rainfall-induced landslides, Appl. Math. Model., 80 (2020), 408–425.
- [25] C. Yang and J. Hou, Jacobi spectral approximation for boundary value problems of nonlinear fractional pantograph differential equations, Numer. Algor., 86 (2021), 1089–1108.
- [26] X. J. Yang, General Fractional Derivatives: Theory, Methods and Applications, CRC Press Taylor & Francis Group, 2019.
- [27] X. Yu, L. Li, and Z. Wang, Efficient space-time Legendre rational spectral method for parabolic problems in unbounded domains, Appl. Numer. Math., 170 (2021), 39–54.
- [28] M. A. Zaky, A Legendre spectral quadrature tau method for the multi-term time-fractional diffusion equations, Comp. Appl. Math., 37 (2018), 3525–3538.
- [29] M. Zayernouri and G. Karniadakis, Fractional spectral collocation method, SIAM J. Sci. Comput., 36 (2014), 40–62.
- [30] B. Zhang, W. Bu, and A. Xiao, Efficient difference method for time-space fractional diffusion equation with Robin fractional derivative boundary condition, Numer. Algor., 88 (2021), 1965–1988.
- [31] T. Zhang, H. Li, and Z. Wang, Efficient space-time Jacobi rational spectral methods for second order timedependent problems on unbounded domains, Appl. Numer. Math., 176 (2022), 159–181.
- [32] M. Zheng, Z. Jin, F. Liu, and V. Anh, Matrix transfer technique for anomalous diffusion equation involving fractional Laplacian, Appl. Numer. Math., 172 (2022), 242–258.
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