Fractional-order boundary value problems with Katugampola fractional integral conditions

Abstract

Abstract In this paper, we study existence (uniqueness) of solutions for nonlinear fractional differential equations with Katugampola fractional integral conditions. Several fixed point theorems are used for sufficient conditions of existence (uniqueness) solutions of nonlinear differential equations such as Banach’s contraction principle, the Leray–Schauder nonlinear alternative, and Krasnoselskii’s fixed point theorem. Applications of the main results are also presented.

Keywords

• Fractional differential equations
• Katugampola derivative
• Integral boundary conditions