Kalita, HemantaGolmankhane, Aireza K.Hazarika, Bipan2025-05-102025-05-1020250354-98362334-716310.2298/TSCI240719003K2-s2.0-105001642211https://doi.org/10.2298/TSCI240719003KIn this work, a new integral so called *F alpha-integral with respect to local fractal derivatives are introduced. Several properties of *F alpha-integrals are discussed. Fundamental theorem for *F alpha-integrable functions is also introduced. A relationship ofF alpha and *F alpha integral is shown. Finally, as an application we solve fractal differential equation D alpha F[S alpha F (x)] = f[t, S alpha F (x)] with S alpha F(tau) = xi in sense of *F alpha-integral.eninfo:eu-repo/semantics/openAccessFractal CalculusFractal Differential EquationGauge Integral Ams (2010)Article291Q4Q3691711WOS:001476283200022