Eur. Phys. J. Plus (2019) 134: 360
https://doi.org/10.1140/epjp/i2019-12769-8

Regular Article

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

¹ Department of Mathematics & Statistics, Jordan University of Science and Technology, P.O. Box 3030, 22110, Irbid, Jordan
² Department of Mathematics, Faculty of Science, The University of Jordan, 11942, Amman, Jordan
³ Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University (KAU), 21589, Jeddah, Saudi Arabia
⁴ Department of Mathematics, Cankaya University, Ankara, Turkey
⁵ Institute of Space Sciences, Magurele, Bucharest, Romania

^* e-mail: iajaradat@just.edu.jo

Received: 26 January 2019
Accepted: 17 May 2019
Published online: 26 July 2019

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 -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 -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 -models are solved and the presence of remnant memory, due to the fractional derivatives, is graphically illustrated.