SOLVABILITY FOR INFINITE SYSTEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SEQUENCE SPACES $l_{p}$ AND $c_{0}$

Abstract

‎This paper is devoted to an infinite system of nonlinear fractional differential equations in the Banach spaces $c_{0}$ and $l_ p$ with $p\geq 1.$ Existence results are obtained‎, ‎by using the theory of measure of noncompactness and a new generalization of Darbo's fixed point theorem‎. ‎Some examples are also included to show the efficiency of our results‎.