TY - JOUR
TI - An introduction to q-Henstock-Kurzweil integral and applications
AU - Zengin Gülizar Gülenay
AU - Savaş Ekrem
AU - Kalita Hemanta
AU - Bharali Hemen
JN - Thermal Science
PY - 2026
VL - 30
IS - 1
SP - 317
EP - 336
PT - Article
AB - 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.
DO - 10.2298/TSCI250409171Z
ER -