Regulated functions space R(R+,R∞) and its application to some infinite systems of fractional differential equations via family of measures of noncompactness

Abstract

We study the solvability of following infinite systems of fractional boundary value problem {cD?ui(t) = fi(t, ui(t))), ? ? (n ? 1, n), 0 < t < +?, ui(0) = 0, uq i (0) = 0, cD??1ui(?) = ?m?2,j=1 ?jui(?j). The purpose of this work is to present a new family of measures of noncompactness in the regulated function spaces R(R+,R?) on unbounded interval and a fixed point theorem of Darbo type. Finally, we give an example to show the effectiveness of the obtained result.