[1] Abdelhedi, W.: Fractional differential equations with a \begin{document}$ \psi $\end{document}-Hilfer fractional derivative. Comput. Appl. Math. 40, 53 (2021) [2] Ali, I., Malik, N.A.: Hilfer fractional advection-diffusion equations with power-law initial condition; a numerical study using variational iteration method. Comput. Math. Appl. 68(10), 1161–1179 (2014) [3] Atkinson, C., Osseiran, A.: Rational solutions for the time-fractional diffusion equation. SIAM J. Appl. Math. 71(1), 92–106 (2011) [4] Borhanifar, A., Valizadeh, S.: Mittag-Leffler-Padé approximations for the numerical solution of space and time fractional diffusion equations. Int. J. Appl. Math. Res. 4(4), 466 (2015) [5] Furati, K.M., Mustapha, K., Sarumi, I.O., Iyiola, O.S.: Inverse source in two-parameter anomalous diffusion, numerical algorithms, and simulations over graded time meshes. Comput. Appl. Math. 40(1), 25 (2021) [6] Furati, K.M., Sarumi, I.O., Khaliq, A.Q.M.: Fractional model for the spread of Covid-19 subject to government intervention and public perception. Appl. Math. Modell. 95, 89–105 (2021) [7] Garra, R., Garrappa, R.: The Prabhakar or three parameter Mittag-Leffler function: theory and application. Commun. Nonlinear Sci. Num. Simul. 56, 314–329 (2018) [8] Garra, R., Gorenflo, R., Polito, F., Tomovski, Z.: Hilfer-Prabhakar derivatives and some applications. Appl. Math. Comput. 242, 576–589 (2014) [9] Garrappa, R.: Numerical evaluation of two and three parameter Mittag-Leffler functions. SIAM J. Numer. Anal. 53(3), 1350–1369 (2015) [10] Garrappa, R., Mainnardi, F.: Models of dielectric relaxation based on completely monotone functions. Fract. Calc. Appl. Anal. 19(5), 1105–1160 (2016) [11] Garrappa, R., Popolizio, M.: Generalized exponential time differencing methods for fractional order problems. Comput. Math. Appl. 62, 876–890 (2011) [12] Gorenflo, R., Kilbas, A.A., Mainardi, F., Rogosin, S.V.: Mittag-Leffler Functions Related Topics and Applications. Springer, Berlin (2014) [13] Gorenflo, R., Loutchko, J., Luchko, Y.: Computation of the Mittag-Leffler function \begin{document}$ E_{\alpha,\beta }(z) $\end{document} and its derivative. Fract. Calc. Appl. Anal. 5(4), 491–518 (2002) [14] Ingo, C., Barrick, T.R., Webb, A.G., Ronen, I.: Accurate Padé global approximations for the Mittag-Leffler function, its inverse, and its partial derivatives to efficiently compute convergent power series. Int. J. Appl. Comput. Math. 3(2), 347–362 (2017) [15] Iyiola, O.S., Asante-Asamani, E.O., Wade, B.A.: A real distinct poles rational approximation of generalized Mittag-Leffler functions and their inverses: applications to fractional calculus. J. Comput. Appl. Math. 330, 307–317 (2018) [16] Kilbas, A.A., Srivastava, H.M., Trujullo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006) [17] Luchko, Y., Gorenflo, R.: An operational method for solving fractional differential equations with the Caputo derivatives. Acta Math. Vietnamica 24, 207–233 (1999) [18] Pandey, S.C.: The Lorenzo-Hartley’s function for fractional calculus and its applications pertaining to fractional order modelling of anomalous relaxation in dielectrics. Comput. Appl. Math. 37, 2648–2666 (2018). https://doi.org/10.1007/s40314-017-0472-7 [19] Sarumi, I.O.: Reaction coefficient identification problem for a time-fractional diffusion equation. In: 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), Ajman, United Arab Emirates, pp. 1–6 (2023) [20] Sarumi, I.O., Furati, K.M., Khaliq, A.Q.M.: Highly accurate global Padé approximations of generalized Mittag-Leffler function and its inverse. J. Sci. Comput. 82, 46 (2020) [21] Sarumi, I.O., Furati, K.M., Khaliq, A.Q.M., Mustapha, K.: Generalized exponential time differencing schemes for stiff fractional systems with nonsmooth source term. J. Sci. Comput. 86, 23 (2021). https://doi.org/10.1007/s10915-020-01374-y [22] Stanislavsky, A., Weron, K.: A typical case of the dielectric relaxation responses and its fractional kinetic equation. Fract. Calc. Appl. Anal. 19(1), 212–228 (2016) [23] Starovoïtov, A.P., Starovoïtova, N.A.: Padé approximants of the Mittag-Leffler functions. Sbornik Math. 198(7), 1011–1023 (2007) [24] Vieira, N., Rodrigues, M.M., Ferreira, M.: Time-fractional diffusion equation with \begin{document}$ \psi $\end{document}-Hilfer derivative. Comput. Appl. Math. 41(6), 230 (2022) [25] Winitzki, S.: Uniform approximations for transcendental functions. In: Kumar, V., Gavrilova, M.L., Jeng Kenneth Tan, C., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003, pp. 780–789. Springer, Berlin, Heidelberg (2003) [26] Zakariya, Y.F., Afolabi, Y.O., Nuruddeen, R.I., Sarumi, I.O.: Analytical solutions to fractional fluid flow and oscillatory process models. Fractal Fract. 2(18), 1–12 (2018) [27] Zeng, C.B., Chen, Y.Q.: Global Padé approximations of the generalized Mittag-Leffler function and its inverse. Fract. Calc. Appl. Anal. 18(6), 1492–1506 (2015) [28] Zeng, F., Zhang, Z., Karniadakis, G.E.: Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions. Comput. Methods Appl. Mech. Engrg. 327(1), 478–502 (2017) |