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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Bibliographic Details
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
Description
Summary: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.
ISSN:1018-3647

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