Operational Methods With Applications In Fractional Calculus
Résumé
In this study, after introducing some properties of the Laplace and Stieltjes transforms, we consider certain fractional differential equations, evaluation of certain new indefinite integrals and sums of special functions, singular integro-differential equation where the fractional derivative is in the Caputo-Fabrizio sense. Some constructive examples are also provided.
Téléchargements
Les données sur le téléchargement ne sont pas encore disponible.
Références
\bibitem{1} A.Aghili,{ \it Direct methods for singular integral equations and non-homogeneous parabolic PDEs}, J. Numer. Anal. Approx. Theory, vol. 51 (2022) no. 2, pp.109-123, doi.org/10.33993/jnaat512-1269.
ictp.acad.ro/jnaat.
\bibitem{2} A.Aghili, {\it Some results involving the Airy functions and Airy transforms}, Tatra Mt. Math. Publ. 79(2021), 13-32, DOI: 10.2478/tmmp-2021-0017.
\bibitem{3} A.Aghili, {\it Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method}, Applied Mathematics and Nonlinear Sciences, 2020 (aop) 1-12.
\bibitem{4} A.Aghili, {\it Solution to time fractional non-homogeneous first order PDE with non-constant coefficients},Tbilisi Mathematical Journal 12(4) (2019),pp. 149-155.
\bibitem{5} A.Apelblat, {\it Laplace transforms and their applications}, Nova science publishers, Inc, New York, 2012.
\bibitem{6} D. Brown, J.Maceli, O.Yurekli, {\it Identities and Parseval type relations for the $\mathcal{L}_2$-transform}, Applied Mathematics And Computation, 196 (2008) 426-432.
\bibitem{7} H. J. \ Glaeske, A.P.\ Prudnikov, K. A.\ Skornik, {\it Operational calculus and related topics},Chapman and Hall / CRC 2006.
\bibitem{8} I.S.Gradshteyn, I.M. Ryzhik, (1980).{\it Table of integrals, series and products}, Academic Press, NY.
\bibitem{9} N.N. Lebedev, {\it Special functions and their applications}, 1972. Prentice-Hall, INC.
\bibitem{10} B. Patra, {\it An introduction to integral transforms}, CRC press, 2016.
\bibitem{11} I. Podlubny,{\it Fractional differential equations}, Academic Press, San Diego, CA,1999.
ictp.acad.ro/jnaat.
\bibitem{2} A.Aghili, {\it Some results involving the Airy functions and Airy transforms}, Tatra Mt. Math. Publ. 79(2021), 13-32, DOI: 10.2478/tmmp-2021-0017.
\bibitem{3} A.Aghili, {\it Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method}, Applied Mathematics and Nonlinear Sciences, 2020 (aop) 1-12.
\bibitem{4} A.Aghili, {\it Solution to time fractional non-homogeneous first order PDE with non-constant coefficients},Tbilisi Mathematical Journal 12(4) (2019),pp. 149-155.
\bibitem{5} A.Apelblat, {\it Laplace transforms and their applications}, Nova science publishers, Inc, New York, 2012.
\bibitem{6} D. Brown, J.Maceli, O.Yurekli, {\it Identities and Parseval type relations for the $\mathcal{L}_2$-transform}, Applied Mathematics And Computation, 196 (2008) 426-432.
\bibitem{7} H. J. \ Glaeske, A.P.\ Prudnikov, K. A.\ Skornik, {\it Operational calculus and related topics},Chapman and Hall / CRC 2006.
\bibitem{8} I.S.Gradshteyn, I.M. Ryzhik, (1980).{\it Table of integrals, series and products}, Academic Press, NY.
\bibitem{9} N.N. Lebedev, {\it Special functions and their applications}, 1972. Prentice-Hall, INC.
\bibitem{10} B. Patra, {\it An introduction to integral transforms}, CRC press, 2016.
\bibitem{11} I. Podlubny,{\it Fractional differential equations}, Academic Press, San Diego, CA,1999.
Publiée
2026-03-13
Rubrique
Special Issue: Advanced Computational Methods for Fractional Calculus
Copyright (c) 2026 Boletim da Sociedade Paranaense de Matemática
Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
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).
