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

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

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.

Suggested Citation

  • Jaradat, Imad & Alquran, Marwan & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2022. "Analytic simulation of the synergy of spatial-temporal memory indices with proportional time delay," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
  • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000297
    DOI: 10.1016/j.chaos.2022.111818
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    References listed on IDEAS

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