Battery discharging model on fractal time sets

Abstract

This article is devoted to propose and investigate the fractal battery discharging model, which is one of the well-known models with a memory effect. It is presented as to how non-locality affects the behavior of solutions and how the current state of the system is affected by its past. Firstly, we present a local fractal solution. Then we solve the non-local fractal differential equation and examine the memory effect that includes the Mittag-Leffler function with one parameter. For that aim, the local fractal and non-local fractal Laplace transforms are used to achieve fractional solutions. In addition, the simulation analysis is performed by comparing the underlying fractal derivatives to the classical ones in order to understand the significance of the results. The effects of the fractal parameter and the fractional parameter are discussed in the conclusion section.