The investigation of a classical particle in the presence of fractional calculus

Abstract

In this article, by applying a preliminary and comprehensive definition of the fractional calculus, its effect on different aspects of physics is specified, as in the case of Laplace transforms, Riemann-Liouville, and Caputo derivatives. Applications of the fractional calculus in studying the dynamics of particle motion in classical mechanics are investigated analytically. Furthermore, we compare our results with those obtained from the usual methods and we show that both solutions coincide provided the fractional effects are removed.