Modeling Exponential Growth and Exponential Decay Real Phenomena by Ψ-Caputo Fractional Derivative
M. Awadalla *
Department of Electrical and Electronic Engineering, Girne American University, Girne, Via Mersin 10, Turkey
Y. Y. Yameni
Department of Mathematics, Eastern Mediterranean University, Famagusta, Via Mersin 10, Turkey
*Author to whom correspondence should be addressed.
Abstract
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 
. 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.
Keywords: Exponential decay, exponential growth, Ψ-Caputo fractional derivative, optimization, initial value problems