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

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.

Keywords

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