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International Journal of Applied Mathematics and Computer Science

The Journal of University of Zielona Gora and Lubuskie Scientific Society

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An operational Haar wavelet method for solving fractional Volterra integral equations

Habibollah Saeedi1, / Nasibeh Mollahasani1, / Mahmoud Moghadam1 / Gennady Chuev1,

Department of Mathematics, Faculty of Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran1

Max Planck Institute for Mathematics in the Sciences (MIS), Inselstrasse 22, Leipzig 04103, Germany2

Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran3

Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russia4

This content is open access.
(CC BY-NC-ND 4.0)

Citation Information: International Journal of Applied Mathematics and Computer Science. Volume 21, Issue 3, Pages 535–547, ISSN (Print) 1641-876X, DOI: 10.2478/v10006-011-0042-x, September 2011

Publication History:
Published Online:
2011-09-22

An operational Haar wavelet method for solving fractional Volterra integral equations

A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.

Keywords: fractional Volterra integral equation; Abel integral equation; fractional calculus; Haar wavelet method; operational matrices

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