THERMAL SCIENCE

International Scientific Journal

Gülizar Gülenay Zengin

,

Ekrem Savaş

,

Hemanta Kalita

,

Hemen Bharali

AN INTRODUCTION TO Q-HENSTOCK-KURZWEIL INTEGRAL AND APPLICATIONS

ABSTRACT
The Jackson integral represents a q-analogue of the Riemann integral, thereby extending the integration concept into the domain of q-calculus, while the Riemann integral remains a traditional calculus tool for assessing the area under a curve. It is well known that Henstock-Kurzweil integral is a generalized Riemann integral. In this article, we introduce q-analogue of Henstock-Kurzweil integral, called q-Henstock-Kurzweil integral. We discuss several important properties of newly introduce q-Henstock-Kurzweil integrals and its some results. Moreover, we show that q-Henstock-Kurzweil integrable functions contain Henstock-Kurzweil integrable functions. Furthermore, we introduce Fundamental Theorem of Calculus for q-Henstock-Kurzweil integrable functions in q-analogous approach. Finally, using this integrable functions we suggest a solution method for a class of linear fractional q-differential equations.
KEYWORDS
q-Henstock-Kurzweil integral, Henstock-Kurzweil integral, q-calculus, q-fractional differential equation
PAPER SUBMITTED: 2025-04-09
PAPER REVISED: 2025-07-27
PAPER ACCEPTED: 2025-09-05
PUBLISHED ONLINE: 2025-11-01
DOI REFERENCE: https://doi.org/10.2298/TSCI250409171Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2026, VOLUME 30, ISSUE No. 1, PAGES [317 - 336]
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An introduction to q-Henstock-Kurzweil integral and applications

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence