<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

An operational Haar wavelet method for solving fractional Volterra integral equations

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

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

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

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

International Journal of Applied Mathematics and Computer Science

A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to...

An operational Haar wavelet method for solving fractional Volterra integral equations

Publié en ligne: 22 sept. 2011

Pages: 535 - 547

DOI: https://doi.org/10.2478/v10006-011-0042-x

Mots clés
fractional Volterra integral equation, Abel integral equation, fractional calculus, Haar wavelet method, operational matrices

This content is open access.

An operational Haar wavelet method for solving fractional Volterra integral equations

Publié en ligne: 22 sept. 2011

Pages: 535 - 547

DOI: https://doi.org/10.2478/v10006-011-0042-x

Mots clésfractional Volterra integral equation, Abel integral equation, fractional calculus, Haar wavelet method, operational matrices

This content is open access.

Mots clés
fractional Volterra integral equation, Abel integral equation, fractional calculus, Haar wavelet method, operational matrices