The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)-Reference-Cited by-同舟云学术

The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)

Published:2023-07-02 Issue:7 Volume:7 Page:525
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Li Qien¹^ORCID,Zhou Yong¹²^ORCID

Affiliation:

1. Faculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, China

2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Abstract

In this study, we investigate the existence of mild solutions for a class of Hilfer fractional stochastic evolution equations with order μ∈(1,2) and type ν∈[0,1]. We prove the existence of mild solutions of Hilfer fractional stochastic evolution equations when the semigroup is compact as well as noncompact. Our approach is based on the Schauder fixed point theorem, the Ascoli–Arzelà theorem and the Kuratowski measure of noncompactness. An example is also provided, to demonstrate the efficacy of this method.

Funder

Fundo para o Desenvolvimento das Ci\^{e}ncias e da Tecnologia of Macau

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/7/525/pdf

Reference22 articles.

1. Hilfer, R. (2000). Applications of Fractional Calculus in Physics, World Scientific.

2. Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier Science.

3. Zhou, Y. (2014). Basic Theory of Fractional Differential Equations, World Scientific.