Investigating the Existence Results for Hilfer Fractional Stochastic Evolution Inclusions of Order 1<μ<2

The objective of this article is to investigate the issue of existence results for Hilfer fractional stochastic differential inclusions of order 1 < μ < 2 in Hilbert spaces. Our discussion is based on fractional calculus, multivalued analysis, sine and cosine operators, and Bohnenblust–Karlin’...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2024, Vol.23 (1)
Main Authors: Pradeesh, J., Vijayakumar, V.
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Existence theorems
Fixed points (mathematics)
Fractional calculus
Hilbert space
Inclusions
Mathematics
Mathematics and Statistics
Operators (mathematics)
Stochastic systems
Trigonometric functions
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Summary:The objective of this article is to investigate the issue of existence results for Hilfer fractional stochastic differential inclusions of order 1 < μ < 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 < μ < 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.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-023-00899-5