Approximate Controllability of Hilfer Fractional Stochastic Evolution Inclusions of Order 1 < q < 2

Approximate Controllability of Hilfer Fractional Stochastic Evolution Inclusions of Order 1 < q < 2

This paper addresses the approximate controllability results for Hilfer fractional stochastic differential inclusions of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo&g...

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Bibliographic Details
Main Authors: Anurag Shukla, Sumati Kumari Panda, Velusamy Vijayakumar, Kamalendra Kumar, Kothandabani Thilagavathi
Format: Article
Language:English
Published: MDPI AG 2024-08-01
Series:Fractal and Fractional
Subjects:
approximate controllability
hilfer fractional derivative
multi-valued maps
stochastic theory
fixed point theorem
Online Access:https://www.mdpi.com/2504-3110/8/9/499
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Summary:This paper addresses the approximate controllability results for Hilfer fractional stochastic differential inclusions of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi mathvariant="sans-serif">q</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>. Stochastic analysis, cosine families, fixed point theory, and fractional calculus provide the foundation of the main results. First, we explored the prospects of finding mild solutions for the Hilfer fractional stochastic differential equation. Subsequently, we determined that the specified system is approximately controllable. Finally, an example displays the theoretical application of the results.
ISSN:2504-3110

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