Characterization of non-differentiable points in a function by Fractional derivative of Jumarrie type
There are many functions which are continuous everywhere but not differentiable at some points, like in physical systems of ECG, EEG plots, and cracks pattern and for several other phenomena. Using classical calculus those functions cannot be characterized-especially at the non-differentiable points. To characterize those functions the concept of Fractional Derivative is used. From the analysis it is established that though those functions are unreachable at the non-differentiable points, in classical sense but can be characterized using Fractional derivative. In this paper we demonstrate use of modified Riemann-Liouvelli derivative by Jumarrie to calculate the fractional derivatives of the non-differentiable points of a function, which may be one step to characterize and distinguish and compare several non-differentiable points in a system or across the systems. This method we are extending to differentiate various ECG graphs by quantification of non-differentiable points; is useful method in differential diagnostic. Each steps of calculating these fractional derivatives is elaborated.