Residual Power Series Technique for Simulating Fractional Bagley-Torvik Problems Emerging in Applied Physics

Featured Application: Fractional differential equations play a significant role in modeling certain dynamical systems arising in many fields of applied sciences and engineering. In this paper, the authors develop an attractive analytic-numeric technique, residual power series (RPS) method, for solving fractional Bagley Torvik equations with a source term involving Caputo fractional derivative. In regard to its simplicity, the method can be applicable to a wide class of fractional partial differential equations, fractional fuzzy differential equations, fractional oscillator equations, and so on. Numerical simulation of physical issues is often performed by nonlinear modeling, which typically involves solving a set of concurrent fractional differential equations through effective approximate methods. In this paper, an analytic-numeric simulation technique, called residual power series (RPS), is proposed in obtaining the numerical solution a class of fractional Bagley Torvik problems (FBTP) arising in a Newtonian fluid. This approach optimizes the solutions by minimizing the residual error functions that can be directly applied to generate fractional PS with a rapidly convergent rate. The RPS description is presented in detail to approximate the solution of FBTPs by highlighting all the steps necessary to implement the algorithm in addressing some test problems. The results indicate that the RPS algorithm is reliable and suitable in solving a wide range of fractional differential equations applying in physics and engineering.