AccScience Publishing / IJOCTA / Online First / DOI: 10.36922/IJOCTA026320200
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RESEARCH ARTICLE

Nonlinear Hilfer fractional systems of higher order: Existence and finite controllability analysis

Zeeshana Zahoor1 ,  Abdul Haq1*
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1 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu , India
IJOCTA, 026320200 https://doi.org/10.36922/IJOCTA026320200
Received: 4 August 2026 | Revised: 5 October 2026 | Accepted: 8 October 2026 | Published online: 11 November 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This paper investigates the existence and finite-approximate controllability of higher-order nonlinear Hilfer fractional integrodifferential systems governed by Hilfer fractional derivatives of order 1 < ϱ < 2 with nonlocal initial conditions in Hilbert spaces. An appropriate notion of a mild solution is established by means of the higher-order Hilfer fractional resolvent family. Under suitable hypotheses, the existence of mild solutions is proved by applying Schaefer’s fixed-point theorem. Furthermore, the finite-approximate controllability of the proposed system is established by combining the controllability of the corresponding linear system with a variational approach. The obtained results extend the existing finite-approximate controllability theory for Hilfer fractional systems to the higher-order setting. Finally, an illustrative example is presented to demonstrate the applicability of the theoretical results.

Graphical abstract
Keywords
Hilfer derivative
Integrodifferential system
Fractional resolvent
Mild solution
Finite-approximate controllability
Funding
None.
Conflict of interest
The authors have no relevant interests to declare.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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