Solving Abel integral equations of first kind via fractional calculus

Solving Abel integral equations of first kind via fractional calculus

We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and Computer Algebra System Maple, the exact and approximation val...

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Main Authors: Salman Jahanshahi, Esmail Babolian, Delfim F.M. Torres, Alireza Vahidi
Format: Article
Language:English
Published: Elsevier 2015-04-01
Series:Journal of King Saud University: Science
Subjects:
Abel integral equation
Singular integral equations
Caputo fractional derivatives
Fractional integrals
Online Access:http://www.sciencedirect.com/science/article/pii/S1018364714000780
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spelling doaj-2f6edb8166c847ffb34944700a1394632020-11-24T23:46:54ZengElsevierJournal of King Saud University: Science1018-36472015-04-0127216116710.1016/j.jksus.2014.09.004Solving Abel integral equations of first kind via fractional calculusSalman Jahanshahi0Esmail Babolian1Delfim F.M. Torres2Alireza Vahidi3Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranCenter for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, PortugalDepartment of Mathematics, Shahre Rey Branch, Islamic Azad University, Tehran, IranWe give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and Computer Algebra System Maple, the exact and approximation values of three Abel integral equations are found, illustrating the effectiveness of the proposed approach.http://www.sciencedirect.com/science/article/pii/S1018364714000780Abel integral equationSingular integral equationsCaputo fractional derivativesFractional integrals
collection DOAJ
language English
format Article
sources DOAJ
author Salman Jahanshahi
Esmail Babolian
Delfim F.M. Torres
Alireza Vahidi
spellingShingle Salman Jahanshahi
Esmail Babolian
Delfim F.M. Torres
Alireza Vahidi
Solving Abel integral equations of first kind via fractional calculus
Journal of King Saud University: Science
Abel integral equation
Singular integral equations
Caputo fractional derivatives
Fractional integrals
author_facet Salman Jahanshahi
Esmail Babolian
Delfim F.M. Torres
Alireza Vahidi
author_sort Salman Jahanshahi
title Solving Abel integral equations of first kind via fractional calculus
title_short Solving Abel integral equations of first kind via fractional calculus
title_full Solving Abel integral equations of first kind via fractional calculus
title_fullStr Solving Abel integral equations of first kind via fractional calculus
title_full_unstemmed Solving Abel integral equations of first kind via fractional calculus
title_sort solving abel integral equations of first kind via fractional calculus
publisher Elsevier
series Journal of King Saud University: Science
issn 1018-3647
publishDate 2015-04-01
description We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and Computer Algebra System Maple, the exact and approximation values of three Abel integral equations are found, illustrating the effectiveness of the proposed approach.
topic Abel integral equation
Singular integral equations
Caputo fractional derivatives
Fractional integrals
url http://www.sciencedirect.com/science/article/pii/S1018364714000780
work_keys_str_mv AT salmanjahanshahi solvingabelintegralequationsoffirstkindviafractionalcalculus
AT esmailbabolian solvingabelintegralequationsoffirstkindviafractionalcalculus
AT delfimfmtorres solvingabelintegralequationsoffirstkindviafractionalcalculus
AT alirezavahidi solvingabelintegralequationsoffirstkindviafractionalcalculus
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