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This paper is devoted to an infinite system of nonlinear fractional differential equations in the Banach spaces c0 and `p with p ≥ 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.

Solvability for infinite systems of fractional differential equations in Banach sequence spaces lp and c0