A nonlinear fractional partial integro-differential equation with nonlocal initial value conditions

Chenkuan Li; Reza Saadati; Donal O'Regan; Radko Mesiar; Andrii Hrytsenko

doi:10.1002/mma.9486

A nonlinear fractional partial integro-differential equation with nonlocal initial value conditions

Chenkuan Li, Reza Saadati, Donal O'Regan, Radko Mesiar, Andrii Hrytsenko

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

4 Citations (Scopus)

Abstract

In this work, we study a new nonlinear partial integro-differential equation with nonlocal initial value conditions and investigate the solutions of this equation. By considering an equivalent implicit integral equation via series, we prove the uniqueness of solutions of the equation by Babenko's approach, Banach's contraction principle, and the multivariable Mittag–Leffler function. We also demonstrate the application of our key theorem with an illustrative example.

Original language	English
Pages (from-to)	17010-17019
Number of pages	10
Journal	Mathematical Methods in the Applied Sciences
Volume	46
Issue number	16
DOIs	https://doi.org/10.1002/mma.9486
Publication status	Published - 15 Nov 2023

Keywords

Babenko's approach
Banach's contractive principle
multivariate Mittag–Leffler function
nonlinear partial integro-differential equation

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10.1002/mma.9486

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abstract = "In this work, we study a new nonlinear partial integro-differential equation with nonlocal initial value conditions and investigate the solutions of this equation. By considering an equivalent implicit integral equation via series, we prove the uniqueness of solutions of the equation by Babenko's approach, Banach's contraction principle, and the multivariable Mittag–Leffler function. We also demonstrate the application of our key theorem with an illustrative example.",

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AU - Saadati, Reza

AU - O'Regan, Donal

AU - Mesiar, Radko

AU - Hrytsenko, Andrii

PY - 2023/11/15

Y1 - 2023/11/15

N2 - In this work, we study a new nonlinear partial integro-differential equation with nonlocal initial value conditions and investigate the solutions of this equation. By considering an equivalent implicit integral equation via series, we prove the uniqueness of solutions of the equation by Babenko's approach, Banach's contraction principle, and the multivariable Mittag–Leffler function. We also demonstrate the application of our key theorem with an illustrative example.

AB - In this work, we study a new nonlinear partial integro-differential equation with nonlocal initial value conditions and investigate the solutions of this equation. By considering an equivalent implicit integral equation via series, we prove the uniqueness of solutions of the equation by Babenko's approach, Banach's contraction principle, and the multivariable Mittag–Leffler function. We also demonstrate the application of our key theorem with an illustrative example.

KW - Babenko's approach

KW - Banach's contractive principle

KW - multivariate Mittag–Leffler function

KW - nonlinear partial integro-differential equation

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JF - Mathematical Methods in the Applied Sciences

IS - 16

ER -

A nonlinear fractional partial integro-differential equation with nonlocal initial value conditions

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Keywords

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