Multi-Term Nonlinear Fractal-Orders Delayed Abel Integral Equation: Existence of Solutions, Stability, and Applications

Abstract

In this paper we study a multi-term non-linear fractal orders delayed integral equation of the second kind. We examine the existence of integrable solution x ∈ L₁[0, T]. Under certain assumptions, the uniqueness of this solution will be demonstrated. Additionally, the continuous dependence on the problem’s parameters will be investigated. The Hyers-Ulam stability of the problem itself will be established. Finally, as applications we study two initial value problems of multi-term fractal orders integro-differential equations.