[1] Baeumer, B., Meerschaert, M.M.: Tempered stable Lévy motion and transient super-diffusion. J. Comput. Appl. Math. 233, 2438-2448 (2010)
[2] Cao, J.L., Xiao, A.G., Bu, W.P.: Finite difference/finite element method for tempered time fractional advection-dispersion equation with fast evaluation of Caputo derivative. J. Sci. Comput. 83, 48 (2020)
[3] Carmi, S., Turgeman, L., Barkai, E.: On distributions of functionals of anomalous diffusion paths. J. Stat. Phys. 141, 1071-1092 (2010)
[4] Chen, M.H., Deng, W.H.: Discretized fractional substantial calculus. ESAIM Math. Model. Numer. Anal. 49, 373-394 (2015)
[5] Chen, M.H., Deng, W.H.: High order algorithms for the fractional substantial diffusion equation with truncated Lévy flights. SIAM J. Sci. Comput. 37(2), A890-A917 (2015)
[6] Chen, S., Shen, J., Wang, L.L.: Laguerre functions and their applications to tempered fractional differential equations on infinite intervals. J. Sci. Comput. 74, 1286-1313 (2018)
[7] Chen, Z.Q., Deng, W.H., Xu, P.B.: Feynman-Kac transform for anomalous processes. SIAM J. Math. Anal. 53(5), 6017-6047 (2021)
[8] Deng, W.H., Hou, R., Wang, W.L., Xu, P.B.: Modeling Anomalous Diffusion: From Statistics to Mathematics. World Scientific, Singapore (2020)
[9] Deng, W.H., Li, B.Y., Tian, W.Y., Zhang, P.W.: Boundary problems for the fractional and tempered fractional operators. Multiscale Model. Simul. 16(1), 125-149 (2018)
[10] Deng, W.H., Zhang, Z.J.: Variational formulation and efficient implementation for solving the tempered fractional problems. Numer. Methods Partial. Differ. Eqn. 34(4), 1224-1257 (2018)
[11] Ding, H.F., Li, C.P.: A high-order algorithm for time-Caputo-tempered partial differential equation with Riesz derivatives in two spatial dimensions. J. Sci. Comput. 80, 81-109 (2019)
[12] Dong, H.J., Kim, D.: \begin{document}$ L_p $\end{document}-estimates for time fractional parabolic equations with coefficients measurable in time. Adv. Math. 345, 289-345 (2019)
[13] Guo, B.Y.: The Spectral Methods and Its Applications. World Scientific, Singapore (1998)
[14] Guo, L., Zeng, F.H., Turner, I., Burrage, K., Karniadakis, G.E.: Efficient multistep methods for tempered fractional calculus: algorithms and simulations. SIAM J. Sci. Comput. 41(4), A2510-A2535 (2019)
[15] Hanert, E., Piret, C.: A Chebyshev pseudospectral method to solve the space-time tempered fractional diffusion equation. SIAM J. Sci. Comput. 36, A1797-A1812 (2015)
[16] Hesthaven, J.S., Gottlieb, S., Gottlieb, D.: Spectral Methods for Time-Dependent Problems. Cambridge University Press, Cambridge (2007)
[17] Huang, C., Zhang, Z.M., Song, Q.S.: Spectral method for substantial fractional differential equations. J. Sci. Comput. 74(3), 1554-1574 (2018)
[18] Jin, B.T., Lazarov, R., Zhou, Z.: Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview. Comput. Methods Appl. Mech. Eng. 346, 332-358 (2019)
[19] Jin, B.T., Li, B.Y., Zhou, Z.: Subdiffusion with a time-dependent coefficient: analysis and numerical solution. Math. Comput. 88, 2157-2186 (2019)
[20] Li, C., Deng, W.H.: High order schemes for the tempered fractional diffusion equations. Adv. Comput. Math. 42(3), 543-572 (2016)
[21] Li, C., Deng, W.H., Zhao, L.J.: Well-posedness and numerical algorithm for the tempered fractional differential equations. Discrete Cont. Dyn. B 24(4), 1987-2015 (2019)
[22] Liemert, A., Kienle, A.: Computational solutions of the tempered fractional wave-diffusion equation. Fract. Calc. Appl. Anal. 20(1), 139-158 (2017)
[23] Lin, Y.M., Xu, C.J.: Finite difference/spectral approximations for the time-fractional diffusion equation. J. Comput. Phys. 225, 1533-1552 (2007)
[24] Lischke, A., Kelly, J.F., Meerschaert, M.M.: Mass-conserving tempered fractional diffusion in a bounded interval. Fract. Calc. Appl. Anal. 22(6), 1561-1595 (2019)
[25] McLean, W., Mustapha, K.: A second-order accurate numerical method for a fractional wave equation. Numer. Math. 105(3), 481-510 (2007)
[26] Meerschaert, M.M., Zhang, Y., Baeumer, B.: Tempered anomalous diffusion in heterogeneous systems. Geophys. Res. Lett. 35, L17403 (2008)
[27] Moghaddam, B.P., Machado, J.A.T., Babaei, A.: A computationally efficient method for tempered fractional differential equations with application. Comput. Appl. Math. 37, 3657-3671 (2018)
[28] Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
[29] Sabzikar, F., Meerschaert, M.M., Chen, J.H.: Tempered fractional calculus. J. Comput. Phys. 293, 14-28 (2015)
[30] Sakamoto, K., Yamamoto, M.: Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems. J. Math. Anal. Appl. 382(1), 426-447 (2011)
[31] Shen, J., Tang, T., Wang, L.L.: Spectral Methods: Algorithms, Analysis and Applications. Springer, Berlin (2011)
[32] Stynes, M., O’Riordan, E., Gracia, J.L.: Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation. SIAM J. Numer. Anal. 55(2), 1057-1079 (2017)
[33] Sun, X.R., Li, C., Zhao, F.Q.: Local discontinuous Galerkin methods for the time tempered fractional diffusion equation. Appl. Math. Comput. 365(15), 124725 (2020)
[34] Wang, W., Cherstvy, A.G., Liu, X.B., Metzler, R.: Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise. Phys. Rev. E 102, 012146 (2020)
[35] Wu, X.C., Deng, W.H., Barkai, E.: Tempered fractional Feynman-Kac equation: theory and examples. Phys. Rev. E 93(3), 032151 (2016)
[36] Zayernouri, M., Ainsworth, M., Karniadakis, G.E.: Tempered fractional Sturm-Liouville eigenproblems. SIAM J. Sci. Comput. 37, A1777-A1800 (2015)
[37] Zhang, Z.J., Deng, W.H., Karniadakis, G.E.: A Riesz basis Galerkin method for the tempered fractional Laplacian. SIAM J. Numer. Anal. 56(5), 3010-3039 (2018)
[38] Zhao, T.G.: Efficient spectral collocation method for tempered fractional differential equations. Fract. Fract. 7, 277 (2023)
[39] Zhao, T.G., Xuan, H.Y.: Error analysis of spectral method for the space and time fractional Fokker-Planck equation. In: Li, C.P., Wu, Y.J., Ye, R.S. (eds.) Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis. Chapter V, pp. 83-104 (2013)
[40] Zhao, T.G., Zhao, L.J.: Jacobian spectral collocation method for spatio-temporal coupled Fokker-Planck equation with variable-order fractional derivative. Commun. Nonlinear Sci. Numer. Simul. 124, 107305 (2023)
