Fractional physical models based on falling body problem

Abstract

This article is devoted to investigate the fractional falling body problem relied on Newton's second law. We analyze this physical model by means of Atangana-Baleanu fractional derivative in the sense of Caputo (ABC), generalized fractional derivative introduced by Katugampola and generalized ABC containing the Mittag-Leffler function with three parameters $\mathbb{E}_{\alpha,\mu}^{\gamma}(.)$. For that purpose, the Laplace transform (LT) is utilized to obtain fractional solutions. In order to maintain the dimensionality of the physical parameter in the model, we employ an auxiliary parameter $\sigma$ having a relation with the order of fractional operator. Moreover, simulation analysis is carried out by comparing the underlying fractional derivatives with traditional one to grasp the virtue of the results.

Keywords

• falling body problem
• physical model
• fractional calculus
• non-local operators
• fractional model