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

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, w...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 11; no. 12; p. 2752
Main Authors: Li, Chenkuan, Saadati, Reza, Beaudin, Joshua, Hrytsenko, Andrii
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.06.2023
Subjects:
adomian’s decomposition method
Algorithms
analytic and approximate solution
babenko’s approach
Banach spaces
banach’s contractive principle
Cauchy problems
Decomposition
Differential equations
Function space
Integral equations
Mathematics
multivariate Mittag–Leffler function
Nonlinear equations
Partial differential equations
Uniqueness
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11122752