Cauchy Problem for Non-Autonomous Fractional Evolution Equations

In this paper, we study the solvability of Cauchy problem for a class of non-autonomous fractional evolution equation with Caputo’s fractional derivative of order α∈ (1,2) , which can be applied to model the time dependent coefficients fractional differential systems. We first introduce an operator family and analyze its properties, by the iterative method, we construct a solution to an operator-valued Volterra equation, which is the most critical ingredient to prove solvability of the problem. Finally, based on the solution operators we establish the existence and uniqueness of classical solutions.