Abstract
In this paper, we investigate the existence of mild solutions for neutral Hilfer fractional evolution equations with noninstantaneous impulsive conditions in a Banach space. We obtain the existence results by applying the theory of resolvent operator functions, Hausdorff measure of noncompactness, and Sadovskii’s fixed point theorem. We also present an example to show the validity of obtained results.
Highlights
Fractional calculus primarily involves the description of fractional-order derivatives and integral operators [28]
The Hilfer fractional derivative (HFD), a generalization of the RL fractional derivative was first introduced by Hilfer [4, 11, 15, 16]
Gou and Li [12] proved the existence of mild solutions for Sobolevtype Hilfer fractional evolution equations with boundary conditions
Summary
Fractional calculus primarily involves the description of fractional-order derivatives and integral operators [28]. FDEs involving either RL or Caputo derivative are commonly considered with impulsive conditions for obtaining mild solutions [5, 7, 20, 27, 30]. To make a little contribution to existing works, we consider the neutral Hilfer FDEs with impulsive conditions of the mentioned form for obtaining mild solutions. 2, we discuss the Hilfer fractional derivative, Hausdorff measure of noncompactness, and mild solutions of equation (1.1) along with some basic results and lemmas. Definition 2.3 ([13, 31]) A mild solution z ∈ PC1–θ (J , Z) of problem (1.1) is the solution of the corresponding its integral form (2.1) This definition of a mild solution is obtained by means of the Laplace transform of the Hilfer fractional derivative.
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