Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions

Abstract

In this work, the existence of solutions for nonlinear hybrid fractional integro-differential equations involving generalized proportional fractional (GPF) derivative of Caputo-Liouville-type and multi-term of GPF integrals of Reimann-Liouville type with Dirichlet boundary conditions is investigated. The analysis is accomplished with the aid of the Dhage's fixed point theorem with three operators and the lower regularized incomplete gamma function. Further, the uniqueness of solutions and their Ulam-Hyers-Rassias stability to a special case of the suggested hybrid problem are discussed. For the sake of corroborating the obtained results, an illustrative example is presented.

Keywords

• incomplete gamma function
• caputo-liouville proportional fractional derivative
• hybrid fractional integro-differential equation
• fixed point theorem
• ulam-hyers stability