Solvability for an infinite system of fractional order boundary value problems

Abstract

We investigate the solvability for an infinite system of fractional order boundary value problems of differential equations in Banach sequence spaces ${\ell }_{\infty }$ and $\mathbf{c}$. Our approach depends on Darbo’s fixed point theorem in conjunction with new measures of noncompactness in spaces $C^1(J,{\ell }_{\infty })$ and $C^1(J,\mathbf{c})$.