Existence and fractional inequalities for hybrid ρ-Caputo fractional integro-differential equations with non-local conditions

Abstract

This paper focuses on investigating the existence of solutions and fractional inequalities for a hybrid ?-Caputo fractional differential equation accompanied by a non-local condition. By leveraging the Dhage fixed point theorem, we establish specific criteria that guarantee the existence of solutions for our problem. Furthermore, through the application of the ?-Caputo derivative techniques, we illustrate various fractional inequalities.