Nonlocal Conformable-Fractional Differential Equations with a Measure of Noncompactness in Banach Spaces

Mohamed Bouaouid, Mohamed Hannabou, Khalid Hilal and Nasser Saad

Journal of Mathematics, 2020, vol. 2020, 1-6

Abstract: This paper deals with the existence of mild solutions for the following Cauchy problem: dαxt/dtα=Axt+ft,xt,x0=x0+gx,t∈0,τ, where dα./dtα is the so-called conformable fractional derivative. The linear part A is the infinitesimal generator of a uniformly continuous semigroup Ttt≥0 on a Banach space X, f and g are given functions. The main result is proved by using the Darbo–Sadovskii fixed point theorem without assuming the compactness of the family Ttt>0 and the Lipshitz condition on the nonlocal part g.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5615080

DOI: 10.1155/2020/5615080

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