2020
DOI: 10.1002/mma.6347
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An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator

Abstract: The heat equation is parabolic partial differential equation and occurs in the characterization of diffusion progress. In the present work, a new fractional operator based on the Rabotnov fractional-exponential kernel is considered. Next, we conferred some fascinating and original properties of nominated new fractional derivative with some integral transform operators where all results are significant. The fundamental target of the proposed work is to solve the multi dimensional heat equations of arbitrary ord… Show more

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Cited by 182 publications
(95 citation statements)
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“…and B α i as in (15), where the proposed operational matrix represents a kind of unification of ordinary and fractional case.…”
Section: Theorem 1 Assume That the Chebyshev Row Vector T(x) Is Reprementioning
confidence: 99%
See 1 more Smart Citation
“…and B α i as in (15), where the proposed operational matrix represents a kind of unification of ordinary and fractional case.…”
Section: Theorem 1 Assume That the Chebyshev Row Vector T(x) Is Reprementioning
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 works addressed unsteady governing equations for stretching permeable sheets using HAM (Homotopy Analysis Method) [44][45][46][47]. Some other interesting analytical solution for different applicable mathematical problems could be found in [48][49][50][51][52][53][54][55][56].…”
Section: Introductionmentioning
confidence: 99%
“…The nonlinear term yy x serves as an energy stabilizer by transmitting it between small and large scales [6]. The nonlinear evolution equations have attracted a considerable amount of research work in recent years [7][8][9][10][11][12][13][14][15]. Several numerical and analytical techniques have been proposed for solving these equations [16][17][18][19][20][21][22][23].…”
Section: Introductionmentioning
confidence: 99%