Fourier, Laguerre, Laplace Transforms with applications

• Autorzy: Aghili Arman

Identyfikatory

DOI

10.7862/rf.2021.1

• Języki publikacji: EN

Abstrakty

EN

In this article, the author considered certain time fractional equations using joint integral transforms. Transform method is a powerful tool for solving singular integral equations, integral equation with retarded argument, evaluation of certain integrals and solution of partial fractional differential equations. The obtained results reveal that the transform method is very convenient and effective. Illustrative examples are also provided.

Słowa kluczowe

EN

Fourier transform; Laplace transform; Laguerre transform; singular integral equation; Bessel's functions; fractional heat equation

PL

przekształcenie Fouriera; przekształcenie Laplace'a; przekształcenie Laguerre'a; osobliwe równanie całkowe; funkcje Bessela; równanie przewodnictwa cieplnego

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2021
• Tom: Vol. 44
• Strony: 5--17
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Aghili Arman

• Faculty of Mathematical Sciences, Department of Applied Mathematics, University of Guilan, Rasht, P.O. Box 1841, IRAN

• https://orcid.org/0000-0002-3758-2599

Bibliografia

• [1] A. Aghili, Special functions, integral transforms with applications, Tbilisi Mathematical Journal 12 (1) (2019) 33-44.
• [2] A. Aghili, Space-fractional transport equation, Konuralp Journal of Mathematics, 8 (2) (2020) 304-312.
• [3] A. Aghili, Some identities for Mellin, Kontorvich-Lebedev transforms with applications, Tbilisi Mathematical Journal 14 (2) (2021).
• [4] A. Aghili, H. Zeinali, Advances in Laplace type integral transforms with applications, Indian Journal of Science and Technology 7 (6) (2014) 877-890.
• [5] A. Aghili. New results involving Airy polynomials, fractional calculus and solution to generalized heat equation. New trends in mathematical sciences. Vol. 3, 2015. Fourier, Laguerre, Laplace Transforms with Applications
• [6] A. Aghili, B. Salkhordeh Mogaddam, Laplace transform pairs of N-dimensions and second order linear partial di_erential equations with constant coefficients, Annales Mathematicae et Informaticae 35 (2008) 3-10, http://www.ektf.hu/ami
• [7] A. Apelblat, Laplace Transforms and Their Applications, Nova science publishers Inc., New York, 2012.
• [8] S. Das, A note on fractional diffusion equations, Chaos, Solitons and Fractals 42 (2009) 2074-2079.
• [9] B. Davies, Integral Transforms and Their Applications, Springer, USA, 2001.
• [10] F. Mainardi, The fundamental solutions for the fractional diffusion-wave equation, Appl. Math. Lett. (1996) 9:23-8.
• [11] F. Mainardi, Y. Luchko, G. Pagnini, The fundamental solutions the space-time fractional diffusion-wave equation, Fract. Calculus Appl. Anal. 2001:4:153-92.
• [12] I. Podlubny., Fractional Differential Equations, Academic Press, San Diego, CA, 1999.
• [13] R.S. Strichartz, A Guide to Distribution Theory and Fourier Transforms, World Scientific Publishing Co.Pte. Ltd., 2003.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).