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

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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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Authors and Affiliations

  1. Department of Mathematics & Statistics, Jordan University of Science and Technology, P.O. Box 3030, 22110, Irbid, Jordan

    Imad Jaradat & Marwan Alquran

  2. Department of Mathematics, Faculty of Science, The University of Jordan, 11942, Amman, Jordan

    Feras Yousef & Shaher Momani

  3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University (KAU), 21589, Jeddah, Saudi Arabia

    Shaher Momani

  4. Department of Mathematics, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  5. Institute of Space Sciences, Magurele, Bucharest, Romania

    Dumitru Baleanu

Authors
  1. Imad Jaradat
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  2. Marwan Alquran
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  3. Feras Yousef
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  4. Shaher Momani
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  5. Dumitru Baleanu
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Correspondence to Imad Jaradat.

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Jaradat, I., Alquran, M., Yousef, F. et al. On (2 + 1)-dimensional physical models endowed with decoupled spatial and temporal memory indices⋆. Eur. Phys. J. Plus 134, 360 (2019). https://doi.org/10.1140/epjp/i2019-12769-8

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  • DOI: https://doi.org/10.1140/epjp/i2019-12769-8

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