1. Boris, B., Mark, M.: Tempered stable Lévy motion and transient super-diffusion. J. Comput. Appl. Math. 233, 2438–2448 (2010) 2. Cartea, A., del-Castillo-Negrete, D.: Fractional diffusion models of option prices in markets with jumps. Phys. A. 374, 749–763 (2007) 3. Çelik, C., Duman, M.: Crank–Nicolson method for the fractional diffusion equation with the Riesz fractional derivative. J. Comput. Phys. 231, 1743–1750 (2012) 4. Chen, M.H., Deng, W.H.: Fourth order difference approximations for space Riemann–Liouville derivatives based on weighted and shifted Lubich difference operators. Commun. Comput. Phys. 16, 516– 540 (2014) 5. Chen, M.H., Deng, W.H.: A second-order accurate numerical method for the space-time tempered fractional diffusion-wave equation. Appl. Math. Lett. 68, 87–93 (2017) 6. Deng, W.H., Chen, M.H., Barkai, E.: Numerical algorithms for the forward and backward fractional Feynman–Kac equations. J. Sci. Comput. 62, 718–746 (2015) 7. Dehghan, M., Abbaszadeh, M., Deng, W.H.: Fourth-order numerical method for the space-time tempered fractional diffusion-wave equation. Appl. Math. Lett. 73, 120–127 (2017) 8. 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) 9. Ding, H.F.: A high-order numerical algorithm for two-dimensional time-space tempered fractional diffusion-wave equation. Appl. Numer. Math. 135, 30–46 (2019) 10. Gao, G.H., Sun, Z.Z., Zhang, H.W.: A new fractional numerical differentiation formula to approximate the Caputo fractional dreivative and its applications. J. Comput. Phys. 259, 33–50 (2014) 11. Guan, W.H., Cao, X.N.: The implicit midpoint method for Riesz tempered fractional advection-diffusion equation. J. Numer. Methods Comput. 41, 51–65 (2020) 12. He, J.Q., Dong, Y., Li, S.T., Liu, H.L., Yu, Y.J., Jin, G.Y., Liu, L.D.: Study on force distribution of the tempered glass based on laser interference technology. Optik 126, 5276–5279 (2015) 13. Hu, D.D., Cao, X.N.: The implicit midpoint method for Riesz tempered fractional diffusion equation with a nonlinear source term. Adv. Differ. Equ. 2019, 66 (2019) 14. Li, C., Deng, W.H., Wu, Y.J.: Numerical analysis and physical simulations for the time fractional radial diffusion equation. Comput. Math. Appl. 62, 1024–1037 (2011) 15. Li, C., Deng, W.H.: High order schemes for the tempered fractional diffusion equations. Adv. Comput. Math. 42, 543–572 (2016) 16. Magin, R.: Fractional Calculus in Bioengneering. Begell House Publishers, Danbury (2006) 17. Meerschaert, M.M., Zhang, Y., Baeumer, B.: Tempered anomalous diffusion in heterogeneous systems. Geophys. Res. Lett. 35(17), L17403 (2008) 18. Moghaddam, B.P., Tenreiro Machado, J.A., Babaei, A.: A computationally efficient method for tempered fractional differential equations with application. Comput. Appl. Math. 37, 3657–3671 (2017) 19. Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1998) 20. Qiu, Z.S., Cao, X.N.: Second-order numerical methods for the tempered fractional diffusion equations. Adv. Differ. Equ. 2019, 485 (2019) 21. Rosenau, P.: Tempered diffusion: a transport process with propagating fronts and inertial delay. Phys. Rev. A. 46, 7371–7374 (1992) 22. Shen, S.J., Liu, F.W., Anh, V., Turner, I.: The fundamental solution and numerical solution of the Riesz fractional advection-dispersion equation. Math. Comput. 73, 850–872 (2008) 23. Shen, S.J., Liu, F.W., Anh, V.: Numerical approximations and solution techniques for the space-time Riesz–Caputo fractional advection-diffusion equation. Numer. Algor. 56, 383–403 (2011) 24. Sabzikar, F., Meerschaert, M.M., Chen, J.H.: Tempered fractional calculus. J. Comput. Phys. 293, 14–28 (2015) 25. Sun, X.R., Zhao, F.Q., Chen, S.P.: Numerical algorithms for the time-space tempered fractional Fokker–Planck equation. Adv. Differ. Equ. 2017, 259 (2017) 26. Wu, X.C., Deng, W.H., Barkai, E.: Tempered fractional Feynman–Kac equation: theory and examples. Phys. Rev. E. 93, 032151 (2016) 27. Yu, Y.Y., Deng, W.H., Wu, Y.J.: Third order difference schemes (without using points outside of the domain) for one side space tempered fractional partial differential equations. Appl. Numer. Math. 112, 126–145 (2017) 28. Zhuang, P., Liu, F.W., Anh, V., Turner, I.: Numerical methods for the variable-order fractional advection-diffusion with a nonlinear source term. SIAM J. Numer. Anal. 47, 1760–1781 (2009) 29. Zhang, Y.: Moments for tempered fractional advection-diffusion equations. J. Stat. Phys. 139, 915–939 (2010) 30. Zhang, Y.X., Li, Q., Ding, H.F.: High-order numerical approximation formulas for Riemann–Liouville (Riesz) tempered fractional derivative: construction and application (I). Appl. Math. Comput. 329, 432–443 (2018) |