Exact solution of certain fractional Fredholm and Volterra singular integral equations
DOI :
https://doi.org/10.5269/bspm.76637Résumé
In this article, the author has made every effort to expose the capabilities of integral transformations, as well as special functions, to readers interested in this interesting topic through various examples. Important points that readers will find in this article include the applications of integral transforms in evaluating series and integrals involving the Bessel functions, as well as solving fractional differential equations, partial fractional differential equation and fractional singular integral equation, where the fractional derivatives are in the Caputo-Fabrizio sense. It should be emphasised that none of the issues raised in this work are found in previous references. The proposed methods are illustrated by solving some concrete examples.
Références
[2] A.Aghili, Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method, Applied Mathematics and Nonlinear Sciences, 2020 (aop) 1-12
[3] A.Aghili, Some results involving the Airy functions and Airy transforms, Tatra Mt.Math.Publ.79(2021), 13-32, DOI:102478/tmmp-2021-0017.
[4] A.Apelblat, Laplace transforms and their applications, Nova science publishers, Inc, New York, 2012.
[5] I.S.Gradshteyn, I.M. Ryzhik, (1980). Table of integrals, series and products, Academic Press, NY.
[6] N. N.Lebedev, Special functions and their applications,1972. Prentice-Hall, INC.
[7] B. Patra, An introduction to integral transforms, CRC Press 2016.
[8] I. Podlubny, Fractional differential equations, Academic Press, San Diego, CA,1999.
[9] O. Vallee, M.Soares, Airy Functions and Applications to Physics, Imperial College Press, London (2004)
Téléchargements
Publié
Numéro
Rubrique
Licence
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
Comment citer
