Existence of solutions for Caputo fractional delay differential equations with nonlocal and integral boundary conditions

Abstract

Abstract In this paper, the existence and uniqueness of the solutions of Caputo fractional delay differential equations under nonlocal and integral boundary value conditions are studied. By using the Banach contraction principle and the Burton and Kirk fixed-point theorem, some new conclusions about the existence and uniqueness of solutions are obtained. An example is given to illustrate the main results.

Keywords

• Fractional delay differential equation
• Existence and uniqueness of solutions
• Boundary value problem