Optimized Approximation for Fractional Derivatives of non-Smooth Functions via Generalized Derivatives

There are many functions which are continuous everywhere but not differentiable at some points. In this paper, at first, we proposed a new definition to derive the generalized derivative (GD) of non-smooth functions. Then, to characterize the derivatives of these functions, the concept of fractional derivative is used. In this paper we demonstrate use of modified Caputo derivative to calculate the fractional derivatives of the non-differentiable functions. Finally, for efficiency of our approach one numerical example have been presented