Stability analysis of an implicit fractional integro-differential equation via integral boundary conditions

Mehboob Alam*, Akbar Zada, Thabet Abdeljawad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The primary objective of this research study is to analyze a boundary problem involving Caputo fractional integro-differential equations. The focus is on a differential equation with a nonlinear right-hand side composed of two terms. The stability analysis of a fractional integro-differential equation is presented using Ulam's concept. Furthermore, this research study establishes the correlation between the stated problem and the Volterra integral equation. The investigation proceeds by utilizing the renowned Banach and Krasnoselskii's fixed point theorems to explore the existence and uniqueness of solutions for the problem. Additionally, to provide tangible evidence of the abstract findings, two illustrative examples are presented.

Original languageEnglish
Pages (from-to)501-514
Number of pages14
JournalAlexandria Engineering Journal
Volume87
DOIs
Publication statusPublished - Jan 2024
Externally publishedYes

Keywords

  • Caputo derivative
  • Existence and uniqueness
  • Integral conditions
  • Stability

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