On Generalized Local Fractal Calculus Associate With Gauge Integral and Applications

Abstract

In 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.