Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

2 Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran

Abstract

In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on which the fractional order integration of FLWs are easy to calculate. The approach is used this operational matrix with the collocation points to reduce the under study problem to system of algebraic equations. Convergence of the fractional-order Legendre wavelet basis is demonstrate. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Keywords

Computational Methods for Differential Equations
Volume 5, Issue 2 - Serial Number 2
April 2017
Pages 117-140

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History

  • Receive Date: 10 November 2016
  • Revise Date: 15 March 2017
  • Accept Date: 16 April 2017

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