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On the Uniqueness of the Bounded Solution for the Fractional Nonlinear Partial Integro-Differential Equation with Approximations

Author

Listed:
  • Chenkuan Li

    (Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada)

  • Reza Saadati

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran)

  • Joshua Beaudin

    (Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada)

  • Andrii Hrytsenko

    (Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada)

Abstract

This paper studies the uniqueness of the bounded solution to a new Cauchy problem of the fractional nonlinear partial integro-differential equation based on the multivariate Mittag–Leffler function as well as Banach’s contractive principle in a complete function space. Applying Babenko’s approach, we convert the fractional nonlinear equation with variable coefficients to an implicit integral equation, which is a powerful method of studying the uniqueness of solutions. Furthermore, we construct algorithms for finding analytic and approximate solutions using Adomian’s decomposition method and recurrence relation with the order convergence analysis. Finally, an illustrative example is presented to demonstrate constructions for the numerical solution using MATHEMATICA.

Suggested Citation

  • Chenkuan Li & Reza Saadati & Joshua Beaudin & Andrii Hrytsenko, 2023. "On the Uniqueness of the Bounded Solution for the Fractional Nonlinear Partial Integro-Differential Equation with Approximations," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2752-:d:1173450
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    References listed on IDEAS

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    1. Chenkuan Li & Reza Saadati & Rekha Srivastava & Joshua Beaudin, 2022. "On the Boundary Value Problem of Nonlinear Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
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