The Existence of Solutions for Iw/I-Weighted Iψ/I-Hilfer Fractional Differential Inclusions of Order Iμ/I ∈ with Non-Instantaneous Impulses in Banach Spaces

In this research, we obtain the sufficient conditions that guarantee that the set of solutions for an impulsive fractional differential inclusion involving a w-weighted ψ-Hilfer fractional derivative, D[sub.0,t] [sup.σ,v,ψ,w], of order μ∈(1,2), in infinite dimensional Banach spaces that are not empty and compact. We demonstrate the exact relation between a differential equation involving D[sub.0,t] [sup.σ,v,ψ,w] of order μ ∈(1,2) in the presence of non-instantaneous impulses and its corresponding fractional integral equation. Then, we derive the formula for the solution for the considered problem. The desired results are achieved using the properties of the w-weighted ψ-Hilfer fractional derivative and appropriate fixed-point theorems for multivalued functions. Since the operator D[sub.0,t] [sup.σ,v,ψ,w] includes many types of well-known fractional differential operators, our results generalize several results recently published in the literature. We give an example that illustrates and supports our theoretical results.