[1] Alber, H.D.: Materials with Memory: Initial-Boundary Value Problems for Constitutive Equations with Internal Variables. Springer, Berlin (2006)
[2] Alikhanov, A., Apekov, A., Huang, C.: A high-order difference scheme for the diffusion equation of multi-term and distributed orders. In: Mathematics and Its Applications in New Computer Systems: MANCS-2021, pp. 515–523. Springer (2022)
[3] Alikhanov, A.A.: Boundary value problems for the diffusion equation of the variable order in differential and difference settings. Appl. Math. Comput. 219(8), 3938–3946 (2012)
[4] Alikhanov, A.A.: A new difference scheme for the time fractional diffusion equation. J. Comput. Phys. 280, 424–438 (2015)
[5] Alikhanov, A.A.: Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation. Appl. Math. Comput. 268, 12–22 (2015)
[6] Alikhanov, A.A.: A time-fractional diffusion equation with generalized memory kernel in differential and difference settings with smooth solutions. Comput. Methods Appl. Math. 17(4), 647–660 (2017)
[7] Alikhanov, A.A., Asl, M.S., Huang, C., Khibiev, A.: A second-order difference scheme for the nonlinear time-fractional diffusion-wave equation with generalized memory kernel in the presence of time delay. J. Comput. Appl. Math. 438, 115515 (2024)
[8] Alikhanov, A.A., Huang, C.: A high-order L2 type difference scheme for the time-fractional diffusion equation. Appl. Math. Comput. 411, 126545 (2021)
[9] Amendola, G., Fabrizio, M., Golden, J.M., Amendola, G., Fabrizio, M., Golden, J.: Thermodynamics of Materials with Memory. Springer, Berlin (2021)
[10] Baleanu, D., Agrawal, O.P.: Fractional Hamilton formalism within Caputo’s derivative. Czechoslov. J. Phys. 56(10/11), 1087–1092 (2006)
[11] Boltzmann, L.: Theory of elastic aftereffect [zur theorie der elastischen nachwirkung]. Ann. Der Phys. Und Chem. Erganz 7, 7 (1876)
[12] Boltzmann, L.: Zur theorie der elastischen nachwirkung. Annalen der Physik 241(11), 430–432 (1878)
[13] Caputo, M.: Elasticita e dissipazione. Zanichelli, Bologna (1969)
[14] Carr, P., Geman, H., Madan, D.B., Yor, M.: Stochastic volatility for Lévy processes. Math. Finance 13(3), 345–382 (2003)
[15] Day, W.A.: The Thermodynamics of Simple Materials with Fading Memory, vol. 22. Springer, New York (2013)
[16] Ford, N.J., Yan, Y.: An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data. Fract. Calculus Appl. Anal. 20(5), 1076–1105 (2017)
[17] Gao, G.H., Alikhanov, A.A., Sun, Z.Z.: The temporal second order difference schemes based on the interpolation approximation for solving the time multi-term and distributed-order fractional sub-diffusion equations. J. Sci. Comput. 73, 93–121 (2017)
[18] Gu, X.M., Huang, T.Z., Zhao, Y.L., Lyu, P., Carpentieri, B.: A fast implicit difference scheme for solving the generalized time-space fractional diffusion equations with variable coefficients. Numer. Methods Partial Differential Equations 37(2), 1136–1162 (2021)
[19] Gu, X.M., Wu, S.L.: A parallel-in-time iterative algorithm for Volterra partial integro-differential problems with weakly singular kernel. J. Comput. Phys. 417, 109576 (2020)
[20] Jiang, S., Zhang, J., Zhang, Q., Zhang, Z.: Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations. Commun. Comput. Phys. 21(3), 650–678 (2017)
[21] Kedia, N., Alikhanov, A.A., Singh, V.K.: Numerical methods for solving the robin boundary value problem for a generalized diffusion equation with a non-smooth solution. In: Mathematics and Its Applications in New Computer Systems: MANCS-2021, pp. 219–228. Springer (2022)
[22] Kedia, N., Alikhanov, A.A., Singh, V.K.: Stable numerical schemes for time-fractional diffusion equation with generalized memory kernel. Appl. Numer. Math. 172, 546–565 (2022)
[23] Kedia, N., Alikhanov, A.A., Singh, V.K.: Robust finite difference scheme for the non-linear generalized time-fractional diffusion equation with non-smooth solution. Math. Comput. Simul. 219(C), 337–354 (2024)
[24] Khibiev, A., Alikhanov, A., Huang, C.: A second-order difference scheme for generalized time-fractional diffusion equation with smooth solutions. Comput. Methods Appl. Math. 24(1), 101–117 (2024)
[25] Meerschaert, M.M., Sabzikar, F.: Tempered fractional Brownian motion. Stat. Probab. Lett. 83(10), 2269–2275 (2013)
[26] Meerschaert, M.M., Zhang, Y., Baeumer, B.: Tempered anomalous diffusion in heterogeneous systems. Geophys. Res. Lett. 35(17), L17403-1–L17403-5 (2008)
[27] Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)
[28] Ortigueira, M.D., Machado, J.T.: What is a fractional derivative? J. Comput. Phys. 293, 4–13 (2015)
[29] Podlubny, I.: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Math. Sci. Eng. 198, 340 (1999)
[30] Rabotnov Yu, N.: Elements of Hereditary Solids Mechanics: Translated from the Russian by M. Konyaeva. Mir Publishers, Moscow (1980)
[31] Sabzikar, F., Meerschaert, M.M., Chen, J.: Tempered fractional calculus. J. Comput. Phys. 293, 14–28 (2015)
[32] Sandev, T., Chechkin, A., Kantz, H., Metzler, R.: Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Fract. Calculus Appl. Anal. 18(4), 1006–1038 (2015)
[33] Sun, Z.Z., Wu, X.: A fully discrete difference scheme for a diffusion-wave system. Appl. Numer. Math. 56(2), 193–209 (2006)
[34] Tarasov, V.E.: No violation of the Leibniz rule. No fractional derivative. Commun. Nonlinear Sci. Numer. Simul. 18(11), 2945–2948 (2013)
[35] Tarasov, V.E.: On chain rule for fractional derivatives. Commun. Nonlinear Sci. Numer. Simul. 30(1/2/3), 1–4 (2016)
[36] Taukenova, F., Shkhanukov-Lafishev, M.K.: Difference methods for solving boundary value problems for fractional differential equations. Comput. Math. Math. Phys. 46, 1785–1795 (2006)
[37] Ullah, I., Ahmad, S., Ur Rahman, M., Arfan, M.: Investigation of fractional order tuberculosis (TB) model via Caputo derivative. Chaos Solitons Fractals 142, 110479 (2021)
[38] Wang, Y.M., Ren, L.: A high-order $ L $2-compact difference method for Caputo-type time-fractional sub-diffusion equations with variable coefficients. Appl. Math. Comput. 342, 71–93 (2019)
