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In this paper, we consider the nonlinear Ψ-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of solutions. The acquired results are extended to the nonlocal Ψ-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we obtained. Further, examples are provided in support of the results we got.

In this paper, we investigate the existence of mild solutions to semilinear evolution fractional differential equations with non-instantaneous impulses, using the concepts of equicontinuous ( , )-resolvent operator function ℙ , (t) and Kuratowski measure of non-compactness in Banach space .

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