On the Nonlinear Integro-Differential Equations

Abstract

The goal of this paper is to study the uniqueness of solutions of several nonlinear Liouville–Caputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces. The results derived are new and based on Banach’s contractive principle, the multivariate Mittag–Leffler function and Babenko’s approach. We also provide a few examples to demonstrate the use of our main theorems by convolutions and the gamma function.

Keywords

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