Legendre wavelets method for approximate solution of fractional-order differential equations under multi-point boundary conditions

• Published in: International journal of computer mathematics Vol. 95; no. 5; pp. 998 - 1014
• Main Authors: Xu, Xiaoyong, Xu, Da
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.05.2018; Taylor & Francis Ltd
• Subjects: Boundary conditions; collocation method; Collocation methods; Differential equations; fractional-order differential equation; Legendre wavelet; multi-point boundary conditions; shifted Legendre polynomial; Wavelet analysis
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160.2017.1303139

In this paper, Legendre wavelet collocation method is applied for numerical solutions of the fractional-order differential equations subject to multi-point boundary conditions. The explicit formula of fractional integral of a single Legendre wavelet is derived from the definition by means of the shifted Legendre polynomial. The proposed method is very convenient for solving fractional-order multi-point boundary conditions, since the boundary conditions are taken into account automatically. The main characteristic behind this approach is that it reduces equations to those of solving a system of algebraic equations which greatly simplifies the problem. Several numerical examples are solved to demonstrate the validity and applicability of the presented method.