Uniqueness of Solutions of the Generalized Abel Integral Equations in Banach Spaces

Abstract

This paper studies the uniqueness of solutions for several generalized Abel’s integral equations and a related coupled system in Banach spaces. The results derived are new and based on Babenko’s approach, Banach’s contraction principle and the multivariate Mittag–Leffler function. We also present some examples for the illustration of our main theorems.

Keywords

• Riemann–Liouville fractional integral
• Banach’s fixed point theorem
• Babenko’s approach
• Wright’s generalized Bessel function
• multivariate Mittag–Leffler function