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

• J. Pradeesh ^[1] ; V. Vijayakumar ^[1]
  1. [1] Vellore Institute of Technology
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
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• Resumen

  • 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