A generalization of truncated M-fractional derivative and applications to fractional differential equations

Abstract

In this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important properties of the integer-order derivatives. Finally, we obtain the analytical solutions of some ℳ-series fractional differential equations.

Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

“…The ICs are y(0) = 1, y (0) = 1, and the exact solution is y(x) = x 3 + 1 at α 2 = 1.8, ν 2 = 2, where f (x) = 9 10 + 3e x 4 -3x 4 -x 2 2 + 32.6737x 2.2 -11x 5 10 + 6(-1 + x)(1 + x 3 ) 3 . The matrix representation of equation 47is…”

“…Nonlinear differential (DEs) and integro-differential equations (IDEs) have a great importance in modeling of many phenomena in physics and engineering [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Fractional differential equations involving the Caputo and other fractional derivatives, which are a generalization of classical differential equations, have attracted widespread attention [18][19][20][21][22][23][24][25].…”

New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019-nCoV system

“…Some close relationships of COVID-19 with HIV have been presented in [ 23 ]. Many applications of fractional- or integer-order mathematical models explaining more detailed informations about the real-world problems have been presented in a detailed manner [ 24 – 50 ]. In this paper, we investigate the numerical distributions of 2019-nCoV according to time with the help of several approaching terms of VIM.…”

New Caputo-Fabrizio fractional order SEIASqEqHR model for COVID-19 epidemic transmission with genetic algorithm based control strategy

“…In [21] , Biao Tang et al constructed the paradigm in order to predict the dynamics of the novel coronavirus transmission via the ordinary differential equations. Several problems in the real world can be formulated utilizing fractional-order mathematical paradigms, for example see [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] .…”