Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives

Abstract We discuss existence, uniqueness and stability of solutions of the system of nonlinear fractional differential equations D ∗ α i y i ( t ) = f i ( t , y 1 , … , y n ) , y i ( k ) = c k i , 1 ⩽ i ⩽ n , 1 ⩽ k ⩽ m i , where m i α i ⩽ m i + 1 and D ∗ α i denotes Caputo fractional derivative. Linear and nonlinear systems have been solved using Banach fixed point theorem.