2020
DOI: 10.2478/amns.2020.1.00016
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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 derivat… Show more

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Cited by 176 publications
(81 citation statements)
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“…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…”
Section: Error Estimationmentioning
confidence: 99%
See 1 more Smart Citation
“…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…”
Section: Error Estimationmentioning
confidence: 99%
“…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].…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…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] .…”
Section: Introductionmentioning
confidence: 99%