Fractional differential equations with maxima on time scale via Picard operators

Abstract

In this paper, we prove a result of existence and uniqueness of solutions for the following class of problem of initial value for differential equations with maxima and Caputo?s fractional order on the time scales: c??a u(?) = ?(?, u(?), max ??[a,?] u(?)), ? ? J := [a, b]T, 0 < ? ? 1, u(a) = ?, We used the techniques of the Picard and weakly Picard operators to obtain some data dependency on the parameters results.