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

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.