Nonlocal Fractional Differential Equation On The Half Line in Banach Space

Our aim in this paper is to study the existence of solution sets and its topological structure for non-localfractional differential equations on the half-line in a Banach space using Riemann-Liouville definition. Themain result is based on Meir-Keeler fixed point theorem for condensing operators combined with measure ofnon-compactness. An example is given to illustrate the feasibility of our main result.