Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumps

Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumps

This manuscript explores a new class of Hilfer fractional stochastic differential system, as driven by the Wiener process and Rosenblatt process through the application of non-instantaneous impulsive effects and Poisson jumps. Existence of a mild solution to the considered system is proved. Sufficie...

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Bibliographic Details
Main Authors: Noorah Mshary, Hamdy M. Ahmed, Ahmed S. Ghanem
Format: Article
Language:English
Published: AIMS Press 2024-03-01
Series:AIMS Mathematics
Subjects:
impulsive effect
fractional calculus
stochastic differential system
control theory
semigroup theory
Online Access:https://aimspress.com/article/doi/10.3934/math.2024477?viewType=HTML
Description
Summary:This manuscript explores a new class of Hilfer fractional stochastic differential system, as driven by the Wiener process and Rosenblatt process through the application of non-instantaneous impulsive effects and Poisson jumps. Existence of a mild solution to the considered system is proved. Sufficient conditions for the controllability of the proposed control system are established. To prove our main results, we utilize fractional calculus, stochastic analysis, semigroup theory, and the Sadovskii fixed point theorem. In addition, to illustrate the theoretical findings, we present an example.
ISSN:2473-6988

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