General Fractional Integro-Differential Equation of Order $\varrho\in(2,3]$ Involving Integral Boundary Conditions

Abstract

In this paper, we are interested in studying an integro-differential equation with two-point integral boundary conditions using the Caputo fractional derivative of order $2< \varrho \leq 3$. The considered problem is transformed into an equivalent integral equation. To study existence and uniqueness results, our approaches used is based on two well-known fixed point theorems, Banach contraction and Krasnoselskii's theorems. To illustrate our obtained outcomes, an example is given at the end of this paper.

Keywords

• caputo fractional derivative
• existence result
• integral boundary conditions
• integro-differential equation