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

ABSTRACT

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.

KEYWORDS:

• Legendre wavelet
• fractional-order differential equation
• multi-point boundary conditions
• collocation method
• shifted Legendre polynomial

MR(2000) SUBJECT CLASSIFICATION:

• 34B10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by the National Natural Science Foundation of China [Grant Nos. 11601076,11671131], the Youth Science Foundation of Jiangxi Province [Grant Nos. 20151BAB211004, 20151BAB211012] and the Construct Program of the Key Discipline in Hunan Province.