Existence Solutions for Implicit Fractional Relaxation Differential Equations with Impulsive Delay Boundary Conditions

Abstract

The aim of this paper is to study the existence and uniqueness of solutions for nonlinear fractional relaxation impulsive implicit delay differential equations with boundary conditions. Some findings are established by applying the Banach contraction mapping principle and the Schauder fixed-point theorem. An example is provided that illustrates the theoretical results.

Keywords

• fractional relaxation impulsive implicit differential equations
• Riemann–Liouville fractional derivative
• Liouville–Caputo fractional derivative
• existence
• uniqueness
• fixed point