Analytic simulation of the synergy of spatial-temporal memory indices with proportional time delay

Imad Jaradat, Marwan Alquran, Tukur A. Sulaiman and Abdullahi Yusuf

Chaos, Solitons & Fractals, 2022, vol. 156, issue C

Abstract: In the present work, three space-time trace parameters are appended to physical systems to analytically outline their mutual impact and to characterize the dynamic behaviors of these systems; namely the proportional time delay τ∈(0,1) and the Caputo spatial-temporal fractional derivatives α,β∈(0,1). The adopted analytical approach depends on a novel adaptation of the differential transform method in a higher dimensional fractional space in which the initial value problems (IVPs), under consideration, are transformed into a 2-dimensional recurrence relation. Some central differential transformation theorems in 2-dimensional fractional space are provided to illustrate the influence of the aforementioned parameters. The method has been successfully applied to furnish the solution, in the form of a Cauchy product of absolutely convergent series, for a 2-dimensional extension of advection-dispersion, gas dynamics, convection-diffusion, wave, telegraph, and Klein–Gorden equations. The study concluded that the obtained solutions operate as a homotopic mapping between two states, and the Caputo fractional derivatives can be interpreted as memory indices.

Keywords: Caputo derivative; Space-time PDEs; Time delay; Dual-fractional differential transform (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000297

DOI: 10.1016/j.chaos.2022.111818

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