A Study of an IBVP of Fractional Differential Equations in Banach Space via the Measure of Noncompactness

Abstract

In this article, we are concerned with a very general integral boundary value problem of Riemann–Liouville derivatives. We will study the problem in Banach space. To be more specific, we are interested in proving the existence of a solution to our problem via the measure of noncompactness and Mönch fixed-point theorem. Our study in Banach space contains two nonlinear terms and two different orders of derivatives, ς and τ, such that ς∈1,2 and τ∈0,ς. Our paper ends with a conclusion.

Keywords

• IBVP
• Banach space
• existence of solutions
• Mönch fixed point theorem
• Riemann–Liouville
• fractional derivatives