THERMAL SCIENCE
International Scientific Journal
Thermal Science - Online First
online first only
On generalized local fractal calculus associate with gauge integral and applications
ABSTRACT
In this work, a new integral so called *Fα-integral with respect to local fractal derivatives are introduced. Several properties of *Fα-integrals are discussed. Fundamental theorem for *Fα-integrable functions is also introduced. A relationship of Fα and *Fα integral is shown. Finally, as an application we solve fractal differential equation Dα F (SαF(x)) = f (t, Sα F (x)) with Sα F (τ) = ξ in sense of *Fα-integral.
KEYWORDS
PAPER SUBMITTED: 2024-07-19
PAPER REVISED: 2024-12-01
PAPER ACCEPTED: 2024-12-26
PUBLISHED ONLINE: 2025-02-16
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