Uniqueness of Abel’s Integral Equations of the Second Kind with Variable Coefficients

Abstract

This paper studies the uniqueness of the solutions of several of Abel’s integral equations of the second kind with variable coefficients as well as an in-symmetry system in Banach spaces L(Ω) and L(Ω)×L(Ω), respectively. The results derived are new and original, and can be applied to solve the generalized Abel’s integral equations and obtain convergent series as solutions. We also provide a few examples to demonstrate the use of our main theorems based on convolutions, the gamma function and the Mittag–Leffler function.

Keywords

• partial Riemann–Liouville fractional integral
• Babenko’s approach
• Banach fixed point theorem
• Mittag–Leffler function
• gamma function