An effective approach to solve a system fractional differential equations

Abstract

The manuscript details a numerical method for solving a system of fractional differential equations (SFDEs) based on the Caputo fractional derivative by the Ritz method. To use this method, we transform the SFDEs into an optimization problem and obtain the system of nonlinear algebraic equations. Using polynomials of basis functions, we approximate solutions and obtain the coefficients of polynomial expansions by solving the system of nonlinear equations. We debate the convergence analysis of the proposed technique. Some numerical examples are included to assert the theoretical results and the performance of the numerical approximation.

Keywords

• 35R11
• 65M70
• 91G60