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Numerical Analysis of Iterative Fractional Partial Integro‐Differential Equations

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  • Hayman Thabet
  • Subhash Kendre
  • Subhash Unhale

Abstract

Many nonlinear phenomena are modeled in terms of differential and integral equations. However, modeling nonlinear phenomena with fractional derivatives provides a better understanding of processes having memory effects. In this paper, we introduce an effective model of iterative fractional partial integro‐differential equations (FPIDEs) with memory terms subject to initial conditions in a Banach space. The convergence, existence, uniqueness, and error analysis are introduced as new theorems. Moreover, an extension of the successive approximations method (SAM) is established to solve FPIDEs in sense of Caputo fractional derivative. Furthermore, new results of stability analysis of solution are also shown.

Suggested Citation

  • Hayman Thabet & Subhash Kendre & Subhash Unhale, 2022. "Numerical Analysis of Iterative Fractional Partial Integro‐Differential Equations," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:8781186
    DOI: 10.1155/2022/8781186
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    References listed on IDEAS

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    1. Hayman Thabet & Subhash Kendre & Dimplekumar Chalishajar, 2017. "New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-15, September.
    2. Lijun Zhang & Linghai Zhang & Jie Yuan & C. M. Khalique, 2014. "Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, April.
    3. Rabha W. Ibrahim, 2013. "Existence of Iterative Cauchy Fractional Differential Equation," Journal of Mathematics, Hindawi, vol. 2013, pages 1-7, March.
    4. Lijun Zhang & Linghai Zhang & Jie Yuan & C. M. Khalique, 2014. "Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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