Uniqueness of a nonlinear integro-differential equation with nonlocal boundary condition and variable coefficients

Abstract

This paper studies the uniqueness of solutions to a two-term nonlinear fractional integro-differential equation with nonlocal boundary condition and variable coefficients based on the Mittag-Leffler function, Babenko's approach, and Banach's contractive principle. An example is also provided to illustrate the applications of our theorem.

Keywords: Babenko’s approach; Banach’s contractive principle; Liouville-Caputo integro-differential equation; Mittag-Leffler function.