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Investigating the Existence Results for Hilfer Fractional Stochastic Evolution Inclusions of Order \(1<{\mu }<2\)

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Abstract

The objective of this article is to investigate the issue of existence results for Hilfer fractional stochastic differential inclusions of order \(1<\mu <2\) in Hilbert spaces. Our discussion is based on fractional calculus, multivalued analysis, sine and cosine operators, and Bohnenblust–Karlin’s fixed point theorem. At first, we investigate the existence of a mild solution for the Hilfer fractional stochastic differential system of order \(1<\mu <2\). After that, we developed our system with Sobolev-type, and we provided the existence results of a mild solution for the considered system. Then, the ideas of nonlocal conditions are applied in the Sobolev-type Hilfer fractional stochastic system. Finally, an example is offered in order to illustrate the effectiveness of the main theory.

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  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamilnadu, 632 014, India

    J. Pradeesh & V. Vijayakumar

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  1. J. Pradeesh
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Pradeesh, J., Vijayakumar, V. Investigating the Existence Results for Hilfer Fractional Stochastic Evolution Inclusions of Order \(1<{\mu }<2\). Qual. Theory Dyn. Syst. 23, 46 (2024). https://doi.org/10.1007/s12346-023-00899-5

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