THERMAL SCIENCE

International Scientific Journal

Hemanta Kalita

,

Alireza K. Golmankhanehand

,

Bipan Hazarika

ON GENERALIZED LOCAL FRACTAL CALCULUS ASSOCIATE WITH GAUGE INTEGRAL AND APPLICATIONS

ABSTRACT
In this work, a new integral so called *F α-integral with respect to local fractal derivatives are introduced. Several properties of *F α-integrals are discussed. Fundamental theorem for *F α-integrable functions is also introduced. A relationship of F α and *F α integral is shown. Finally, as an application we solve fractal differential equation D αF[S αF (x)] = f[t, S αF (x)] with S αF(τ) = ξ in sense of *F α-integral.
KEYWORDS
fractal calculus, Fractal differential equation, Gauge integral
PAPER SUBMITTED: 2024-07-19
PAPER REVISED: 2024-12-01
PAPER ACCEPTED: 2024-12-26
PUBLISHED ONLINE: 2025-02-16
DOI REFERENCE: https://doi.org/10.2298/TSCI240719003K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 1, PAGES [691 - 711]
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On generalized local fractal calculus associate with Gauge integral and applications

2025 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