Monotone iterative methods for fractional non-autonomous evolution equations with delay

Abstract

In this paper, we use a monotone iterative technique combined with lower and upper solutions to study the existence and uniqueness of solutions for fractional non-autonomous evolution equations with delay in Banach spaces. Under appropriate monotonicity and measure of noncompactness conditions, we establish the existence of extremal solutions and prove uniqueness within the order interval. These results extend previous work by considering more general functional settings and provide the first systematic treatment of monotone iterative methods for such equations.