Article citationsMore>>

Cheng, X. and Zhong, C. (2005) Existence of Positive Solutions for a Second-Order Ordinary Differential System. Journal of Mathematical Analysis and Applications, 312, 14-23.
https://doi.org/10.1016/j.jmaa.2005.03.016

has been cited by the following article:

• TITLE: Legendre-Weighted Residual Methods for System of Fractional Order Differential Equations

  AUTHORS: Umme Ruman, Md. Shafiqul Islam

  KEYWORDS: Fractional Differential Equations, System of Fractional Order BVPs, Weighted Residual Methods, Modified Legendre Polynomials

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.9, September 27, 2024

  ABSTRACT: The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.