Numerical Approximation of the System of Fractional Differential Equations Using the Fibonacci Wavelet Collocation Method

Abstract

This study uses the Fibonacci wavelet collocation method (FWCM) to solve the system of fractional differential equations. Here, we introduce the innovative Fibonacci wavelet method with the help of an operational matrix of integration generated by the Fibonacci polynomials to compute the approximate solution of the linear and nonlinear fractional differential equations. The Fibonacci wavelet collocation method, initially developed for a system of differential equations of integer order, can approximate the solutions to systems of fractional differential equations of fractional order. This method converts the system of fractional differential equations into a system of algebraic equations. These algebraic equations are then solved using the Newton-Raphson method, and the estimated values of the coefficients are then substituted in the approximation. Numerical outcomes are obtained to illustrate the simplicity and effectiveness of the proposed scheme. The numerical results demonstrate that the method is simple to use and precise. The effectiveness and consistency of the developed strategy’s performance are shown in graphs and tables. The method introduces a potential technique for resolving several linear and nonlinear fractional differential equations. Mathematical software called Mathematica has been used to perform all calculations.