An Operational Haar Wavelet Method for Solving Fractional Volterra Integral Equations.

Habib Allah Saeedi and Nasibeh Mollahasani

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Submission date: 18. Dec. 2009 (revised version: January 2010)
Pages: 18
published in: International journal of applied mathematics and computer science, 21 (2011) 3, p. 535-547 
DOI number (of the published article): 10.2478/v10006-011-0042-x
Bibtex
MSC-Numbers: 45DXX, 26A33, 65T60
Keywords and phrases: Volterra Integra Equation, fractional calculus, Haar Wavelet Method, Operational Matrices
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Abstract:
In this work, the Haar wavelet operational matrix of fractional integration is first obtained. Haar wavelet approximating method is then utilized to reduce the fractional Volterra integral equations (which are also called the weakly-singular linear Volterra integral equations) and in particular the Abel integral equations, to a system of algebraic equations. An error bound is estimated and some numerical examples are included to demonstrate the validity and applicability of the method.