A New Definition of Fractal Derivative and Stability of Fractal Dynamical Systems

Abstract

In this paper, we give a novel definition of the fractal derivative and their integral. If r = 1, the definition coincides with the classical definition of the first derivative. Fractal chain rule, fractal exponential functions, fractal Gronwall's inequality, fractal power series expansions, fractal Laplace transforms, and linear fractal differential systems are presented. We study the stability of dynamical systems relying on the new fractal derivative. Additionally, an example is given to compare to other definitions.