Analytical Solutions to Fractional Fluid Flow and Oscillatory Process Models

Abstract

In this paper, we provide solutions to the general fractional Caputo-type differential equation models for the dynamics of a sphere immersed in an incompressible viscous fluid and oscillatory process with fractional damping using Laplace transform method. We study the effects of fixing one of the fractional indices while varying the other as particular examples. We conclude this article by explaining the dynamics of the solutions of the models.

Keywords

• Caputo derivative
• fluid flow
• Laplace transform
• Mittag-Leffler function
• wright function