A study on the solvability of fractional integral equation in a Banach algebra via Petryshyn's fixed point theorem

Abstract

This study focuses on the nonlinear fractional functional integral equation (FFIE) concerning the Riemann-Liouville operator. In certain weaker conditions, the authors demonstrate that the FFIE has a solution, which is defined within the Banach algebra [Formula: see text]. Our analysis relies on the Petryshyn's fixed point theorem and the notion of measure of non-compactness (MNC). In addition, our results include numerous authors' work under less restrictive conditions. Furthermore, we provide an illustrative example of fractional functional integral equations to support our proven results.

Keywords

• Measure of non-compactness (MNC)
• fractional functional integral equation (FFIE)
• fractional integral
• fixed point theory (FPT)
• 47H08
• 47H10