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On (2+1)-dimensional physical models endowed with decoupled spatial and temporal memory indices(star)

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2019

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Springer Heidelberg

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Abstract

The current work concerns the development of an analytical scheme to handle (2 + 1) -dimensional partial differential equations endowed with decoupled spatial and temporal fractional derivatives (abbreviated by (alpha,beta) -models). For this purpose, a new bivariate fractional power series expansion has been integrated with the differential transform scheme. The mechanism of the submitted scheme depends mainly on converting the (alpha,beta) -model to a recurrence-differential equation that can be easily solved by virtue of an iterative procedure. This, in turn, reduces the computational cost of the Taylor power series method and consequently introduces a significant refinement for solving such hybrid models. To elucidate the novelty and efficiency of the proposed scheme, several (alpha,beta) -models are solved and the presence of remnant memory, due to the fractional derivatives, is graphically illustrated.

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Differential Transform Method, Power-Series Method, Fractional Calculus, Wave-Like, Diffusion, Equations, Propagation, Derivatives, Dispersion

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Jaradat, Imad...et al. (2019). "On (2+1)-dimensional physical models endowed with decoupled spatial and temporal memory indices(star)", European Physical Journal Plus, Vol. 134, No. 7.

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European Physical Journal Plus

Volume

134

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7

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