A new definition of the fractal derivative with classical properties

Overview & Synopsis

In this work, we give a new definition of the fractal derivative and some theorems and the integral of the new fractal derivative and some of the classical properties like the fractal chain rule, new fractal integrals, fractal Laplace transform is obtained and the action of fractal derivatives and integrals to each other are discussed. Finally, an example is given to compare the stability of the fractional differential equation to the new definition and other definitions (Hausdorff derivative, YANG derivative, and Caputo derivative). Through comparison, it is indicated that the stretched exponential stability shall serve as an alternative approach for characterizing the decaying patterns of the non-integer order systems.