Solving Abel integral equations of first kind via fractional calculus

Abstract

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.

This is a preprint of a paper whose final and definite form is in Journal of King Saud University (Science), ISSN 1018-3647. Paper submitted 30/Aug/2014; revised 25/Sept/2014; accepted for publication 29/Sept/2014

References in corpus (3)

• Review of Some Promising Fractional Physical Models
• Fractional Order Optimal Control Problems with Free Terminal Time
• Numerical Approximations of Fractional Derivatives with Applications

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• Existence and Uniqueness of Solution for a Fractional Riemann-Liouville Initial Value Problem on Time Scales
• Uniform asymptotic stability of a fractional tuberculosis model
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• Noether's currents for conformable fractional scalar field theories
• Right fractional Sobolev space via Riemann$-$Liouville derivatives on time scales and an application to fractional boundary value problem on time scales
• Left fractional Sobolev space via Riemann$-$Liouville derivatives on time scales and its application to a fractional boundary value problem on time scales