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.
Unconditionally Convergent Series of Operators on Banach Spaces