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 ∆ ω a u(ϑ) = ζ(ϑ, u(ϑ), max ς∈[a,ϑ] u(ς)), ϑ ∈ J := [a, b] T , 0 < ω ≤ 1, u(a) = ϕ, We used the techniques of the Picard and weakly Picard operators to obtain some data dependency on the parameters results.