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

Chenkuan Li (), Reza Saadati, Joshua Beaudin and Andrii Hrytsenko
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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

Mathematics, 2023, vol. 11, issue 12, 1-13

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.

Keywords: adomian’s decomposition method; banach’s contractive principle; multivariate Mittag–Leffler function; babenko’s approach; analytic and approximate solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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