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

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 (α,β)$\left(\alpha ,\beta \right)$ -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 (α,β)$\left(\alpha ,\beta \right)$ -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 (α,β)$\left(\alpha ,\beta \right)$ -models are solved and the presence of remnant memory, due to the fractional derivatives, is graphically illustrated.