Approximate Analytical Solutions of the Fractional-Order Brusselator System Using the Polynomial Least Squares Method

Abstract

The paper presents a new method, called the Polynomial Least Squares Method (PLSM). PLSM allows us to compute approximate analytical solutions for the Brusselator system, which is a fractional-order system of nonlinear differential equations.

A New Operational Matrix of Fractional Derivatives to Solve Systems of Fractional Differential Equations via Legendre Wavelets

“…The parameters M = 2, k = 0, and α = 0.98 were used. A comparison of our results to the approximate solutions introduced by Bota and Caruntu [16] and Chang and Isah [17] when α = 0.98 is displayed in Figure 4. Finally, we also present the numerical computations for u(t) and v(t) when α = 0.98 in Tables 9 and 10.…”

“…were presented by Chang and Isah using the LWPT [17] and by Bota and Caruntu using the PLSM [16]. These solutions when Table 9.…”

“…Kilbas et al [10] inclusively examined fractional differential and fractional integro-differential equations. In addition, numerical solutions of FDEs and the system of such equations have been presented using the Legendre polynomial operational matrix method [11], Bernstein operational matrix method [12], Genocchi operational matrix method [13], Jacobi operational matrix method [14], Chebyshev wavelet operational matrix method [15], polynomial least squares method (PLSM) [16], Legendre wavelet-like operational matrix method (LWPT) [17], and the Genocchi wavelet-like operational matrix method [18].…”

Approximate solutions for the Bagley-Torvik fractional equation with boundary conditions using the Polynomial Least Squares Method

“…One of the recently method used to compute approximate analytical polynomial solutions for fractional differential equation is the Polynomial Least Squares Method (PLSM). The PLSM has been used by C Bota and B Caruntu in 2015 to compute an approximate analytical solution of the fractional order brusselator system ( [6]). Subsequently the same researchers used the PLSM to find approximate solutions for the quadratic Riccati differential equation of fractional order ( [8]),and other types of equations ( [1]).…”

Optimal Control Based on the Polynomial Least Squares Method

“…In this paper we apply the Polynomial Least Squares Method (PLSM) in order to compute approximate analytical polynomial solutions for a optimal control problems. This method was used by C. Bota and B. Cȃruntu in 2014 to compute approximate analytical solutions for the Brusselator system which is a fractional-order system of nonlinear differential equations [10]. In the following years the accuracy of the method is emphasized by its use in solving several types of differential equations [11][12][13].…”