An Efficient Numerical Approach For Solving Linear Variable-order Fractional Differential Equations

Abstract

This paper aims to a present numerical method for solving a class of linear variable-order fractional boundary value problems. In this equation, some terms with fractional-order and some other ones of the correct degree appear in the equation. In order to handle this equation, we use the idea of the least-squares approximation method and Legendre polynomials. These polynomials constitute a system of the complete and orthogonal set. In recent years, useful mathematical properties have been extensively studied and used in various applications. Moreover, convergence analysis for the technique has also been studied in this manuscript. To demonstrate the validity and applicability of the technique, several numerical examples are provided in this article. Examining the results, we find that the approximations obtained in this paper are very accurate for the problem, and efficiently provide the approximation. The technique used in this article can be easily applied to solve similar problems.

Keywords

• fbvps
• lps
• least-squares approximation approach
• residual error function
• approximate solutions