A New Fractal Derivative and its Properties

Abstract

This study introduces a novel fractal derivative alongside its corresponding integral, delving into essential properties such as the fractal Laplace transform, the fractal chain rule, and derivative operations.We also explore the solution of a linear fractal differential system. Furthermore, we provide two illustrative examples that allow us to compare the proposed fractal differential equation to existing definitions, including the Hausdorff derivative, Caputo derivative, and Yang derivative. This comparative analysis underscores the efficacy of the extended definition for addressing non-integer order differential equations.