Approximate controllability of a semilinear impulsive fractional stochastic integro-differential inclusions with Poisson jumps

Volume 38, Issue 2, pp 263--280 https://dx.doi.org/10.22436/jmcs.038.02.08

Publication Date: December 13, 2024 Submission Date: July 10, 2024 Revision Date: July 25, 2024 Accteptance Date: October 16, 2024

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Authors

K. Nandhaprasadh - Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632 014, Tamil Nadu, India. R. Udhayakumar - Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632 014, Tamil Nadu, India.

Abstract

This work explores the approximate controllability of a semilinear impulsive fractional stochastic integro-differential inclusions with Poisson jumps involving the Caputo fractional derivative of order \(q\in (0,1)\). We consider a class of control systems governed by fractional differential inclusions by using Bohnenblust-Karlin's fixed point theorem and stochastic analysis theory to derive a new set of sufficient conditions for the approximate controllability of a semilinear impulsive fractional stochastic integro-differential inclusions with Poisson jumps. Finally, an example is given to illustrate the results obtained.

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Keywords

• Approximate controllability
• semilinear systems
• mild solutions
• impulsive systems
• Poisson jumps

MSC

•  93B05
•  26A33
•  34A08
•  34K30
•  34G20

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