Rigid plate submerged in a Newtonian fluid and fractional differential equation problems via Caputo fractional derivative

Abstract

The study of fractional variational problems with derivatives in the sense of Caputo is a recent subject in Newtonian fluids. In this article, the homotopy perturbation method (HPM), the variational iteration method (VIM), and the Akbari–Ganji method (AGM) were used to solve linear fractional differential equations order in fluid mechanics and fractional optimal control problems in the sense of Caputo. Achieving an exact solution to these equations has been one of the researchers’ goals; according to the research results, the proposed methods provide an exact solution. Comparing the results obtained by the proposed methods with those obtained by the Shehu method reveals that the present methods are very effective and convenient in applied fields. Also, the VIM and AGM methods are more proper than HPM in solving these equations. The solutions obtained by the proposed methods agree with the solutions available in the literature.