Bounded solutions for boundary value problems for fractional differential equations on a Banach space and the half line

Abstract

In this paper, we prove the existence of solutions for a class of boundary value problems for fractional differential equations involving the Riemann-Liouville fractional derivative with an unbounded interval in Banach spaces. Our main tool is the conjunction of the technique of measures of noncompactness with M\"{o}nch's fixed point theorem and the diagonalization method.