Controllability of implicit neutral tempered fractional systems with state and control delays under explicit parameter bounds

Sivaranjani Ramasamy; Kulandhaivel Karthikeyan; Wafa F Alfwzan; Hasib Khan; Jehad Alzabut; Sivaranjani Ramasamy; Kulandhaivel Karthikeyan; Wafa F Alfwzan; Hasib Khan; Jehad Alzabut

doi:10.3934/math.20261011

AIMS Mathematics

2026, Volume 11, Issue 8: 25140-25169. doi: 10.3934/math.20261011

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Research article

Controllability of implicit neutral tempered fractional systems with state and control delays under explicit parameter bounds

1.
Department of Mathematics, KPR Institute of Engineering and Technology, Avinashi Road, Coimbatore, 641 407, Tamilnadu, India
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia
3.
Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia
4.
Department of Industrial Engineering, OSTIM Technical University, 06374 Ankara, Turkiye

Received: 23 May 2026 Revised: 27 July 2026 Accepted: 29 July 2026 Published: 14 August 2026
MSC : 26A33, 47A10, 47A10, 93B05

This research was carried out to analyze the controllability of tempered Caputo fractional differential equations with state and control delay. The well established concept of fixed point theory and tempered $ \alpha $ resolvent families associated with an analytic $ C_0 $ semi-group operator have been incorporated to find the existence of a control function corresponding to the mild solution, which is a form of equivalent integral equation of the proposed fractional problem. The illustration focuses on verifying the applicability of the proposed controllability theorem and investigating the sensitivity of the controllability constant with respect to the fractional order and the tempering parameter. The obtained results demonstrate how these parameters influence the sufficient controllability condition and the corresponding admissible parameter region.
- controllability,
- fractional derivative,
- fixed point theorem,
- fractional-resolvent operator
Citation: Sivaranjani Ramasamy, Kulandhaivel Karthikeyan, Wafa F Alfwzan, Hasib Khan, Jehad Alzabut. Controllability of implicit neutral tempered fractional systems with state and control delays under explicit parameter bounds[J]. AIMS Mathematics, 2026, 11(8): 25140-25169. doi: 10.3934/math.20261011

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Abstract

This research was carried out to analyze the controllability of tempered Caputo fractional differential equations with state and control delay. The well established concept of fixed point theory and tempered $ \alpha $ resolvent families associated with an analytic $ C_0 $ semi-group operator have been incorporated to find the existence of a control function corresponding to the mild solution, which is a form of equivalent integral equation of the proposed fractional problem. The illustration focuses on verifying the applicability of the proposed controllability theorem and investigating the sensitivity of the controllability constant with respect to the fractional order and the tempering parameter. The obtained results demonstrate how these parameters influence the sufficient controllability condition and the corresponding admissible parameter region.

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