Modeling Exponential Growth and Exponential Decay Real Phenomena by Ψ-Caputo Fractional Derivative

The concept of ‘Ψ - Caputo’ fractional derivative is discussed in this article. This method is based on the fractional derivative in Caputo sense of a function with respect to another function Ψ , called kernel. The kernel function Ψ , is any increasing function such that sin.JPG. Experimental studies are used to support the fact that fractional approach of solving differential equations is often better than the classical ordinary approach. The solution to two exponential decay models and one exponential growth model are built using the classical approach and the kernel approach. Several kernel functions are considered and their performances evaluated.