The Joint Laplace-Hankel Transforms for Fractional Diffusion Equation

• Autorzy: Aghili Arman

Identyfikatory

DOI

10.7862/rf.2024.1

• Języki publikacji: EN

Abstrakty

EN

Operational methods are used to accomplish the solution of certain problems with less effort and in a simple routine way. Laplace transforms can be used to solve certain types of fractional singular integral equation not considered in the literature. In this study, the author implemented an analytical technique the joint Laplace-Hankel transforms to provide the exact solution for a time fractional non-homogeneous diffusion equation with non-constant coefficients in cylindrical coordinates. The obtained results reveal that the joint transform method is very convenient and effective. Certain non trivial integral identities involving Airy functions and modified Bessel functions of the second kind are also provided.

Słowa kluczowe

EN

Laplace transforms; Hankel transform; modified Bessel function; Airy function

PL

transformacja Laplace'a; transformacja Hankela; zmodyfikowana funkcja Bessela; funkcje Airy'ego-Langera

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2024
• Tom: Vol. 47
• Strony: 5--21
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Aghili Arman

• University of Guilan, Faculty of Mathematical Sciences Department of Applied Mathematics, Rasht, Iran

• https://orcid.org/000-0002-3758-2599

Bibliografia

• [1] A. Aghili, Solution to time fractional non-homogeneous first order PDE with non-constant coefficients, Tbilisi Math. J. 12 (4) (2019) 149–155.
• [2] A. Aghili, Complete solution for the time fractional diffusion problem with mixed boundary conditions by operational method, Appl. Math. Nonlinear Sci. April (2020) (aop) 1–12.
• [3] A. Apelblat, Laplace Transforms and Their Applications, Nova Science Publishers, Inc., New York, 2012.
• [4] H.J. Glaeske, A.P. Prudnikov, K.A. Skornik, Operational Calculus and Related Topics, Chapman & Hall / CRC, 2006.
• [5] I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, Seventh Edition, 2007.
• [6] M.H.A. Hassan, Ion distribution function during ion cyclotron resonance heating at the fundamental frequency, Phys. Fluids 31 (1988) 596–601.
• [7] A.A. Kilbas, J.J. Trujillo, Differential equation of fractional order: Methods, results and problems. II, Appl. Anal. 81 (2) (2002) 435–493.
• [8] N.N. Lebedev, Special Functions and Their Applications, Prentice-Hall, Inc., 1972.
• [9] B. Patra, An Introduction to Integral Transforms, CRC Press, 2016.
• [10] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, 1999.
• [11] O. Vallee, M. Suares, Airy Functions and Applications to Physics, World Scientific, Imperial College Press, 2003.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).