Approximate controllability of Hilfer fractional integro-differential neutral dynamical system with infinite delay

Chandrabose Sindhu Varun Bose; Chandrabose Sindhu Varun Bose

doi:10.3934/cam.2026013

Communications in Analysis and Mechanics

2026, Volume 18, Issue 2: 329-365. doi: 10.3934/cam.2026013

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Research article

Approximate controllability of Hilfer fractional integro-differential neutral dynamical system with infinite delay

Chandrabose Sindhu Varun Bose ^,

Department of Mathematics, Faculty of Engineering and Technology, SRM IST Vadapalani Campus, Chennai, 600026, Tamil Nadu, India

Received: 01 September 2025 Revised: 18 December 2025 Accepted: 22 January 2026 Published: 14 April 2026
26A33, 34A08, 47D09

This paper investigates the approximate controllability of Hilfer integro-differential neutral dynamical systems with infinite delay governed by almost sectorial operators. The mild solution of the proposed system is derived using the Laplace transform technique. Subsequently, the approximate controllability of the system is established by the Bohnenblust–Karlin - fixed point theorem. Furthermore, the controllability of the associated neutral system is analyzed in detail. Finally, a numerical example is presented to demonstrate the validity and applicability of the theoretical results and our system explained via a filter system.
- approximate controllability,
- Hilfer fractional derivative,
- almost sectorial operators,
- multivalued maps
Citation: Chandrabose Sindhu Varun Bose. Approximate controllability of Hilfer fractional integro-differential neutral dynamical system with infinite delay[J]. Communications in Analysis and Mechanics, 2026, 18(2): 329-365. doi: 10.3934/cam.2026013

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Abstract

This paper investigates the approximate controllability of Hilfer integro-differential neutral dynamical systems with infinite delay governed by almost sectorial operators. The mild solution of the proposed system is derived using the Laplace transform technique. Subsequently, the approximate controllability of the system is established by the Bohnenblust–Karlin - fixed point theorem. Furthermore, the controllability of the associated neutral system is analyzed in detail. Finally, a numerical example is presented to demonstrate the validity and applicability of the theoretical results and our system explained via a filter system.

References

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