Local fractional Improper integral in fractal space

Abstract

The fractional calculus does with the theory of real (or imaginary) order integral and differential operators and it stands for a natural instrument to model nonlocal phenomena, either in space or time, involving different scales. Local fractional calculus (also called fractal calculus) has played a significant part not only in mathematics but also in physics and engineering. The main purpose of this paper is to establish local fractional improper integrals and an analogue of the classical Dirichlet-Abel test for local fractional improper integrals in fractal space. In the paper, we study local fractional improper integrals on fractal space. By some mean value theorems for local fractional integrals, we prove an analogue of the classical Dirichlet-Abel test for local fractional improper integrals in fractal space.