Certain integral transforms involving Appell and Bessel functions and their applications-Reference-Cited by-同舟云学术

Certain integral transforms involving Appell and Bessel functions and their applications

Published:2023-01-10 Issue:2 Volume:43 Page:105-116
ISSN:0174-4747
Container-title:Analysis
language:en
Short-container-title:

Author:

Belafhal Abdelmajid¹,Nossir Naima¹,Dalil-Essakali Latifa¹,Usman Talha²^ORCID

Affiliation:

1. LPNAMME, Laser Physics Group , Department of Physics , Faculty of Sciences , Chouaïb Doukkali University , P. B 20, 24000 El Jadida , Morocco

2. Department of General Requirements , University of Technology and Applied Sciences , Sur - 411 , Oman

Abstract

Abstract This paper deals with the evaluation of certain integral transforms involving the product of certain Appell and Bessel functions with a weight e - γ ⁢ t 2

{e^{-\gamma t^{2}}}

. The transformations of these integrals are evaluated in terms of the Appell, Kampé de Fériet and the triple hypergeometric functions. As an application, we studied propagation of generalized Humbert–Gaussian beams (GHGBs) and hypergeometric-Gaussian beams (HyGGBs) in turbulent atmosphere and through an ABCD paraxial optical system. The evaluation of these integral transforms has initiated a great interest in mathematical physics and its applications to laser physics and linear or non-linear optics.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anly-2022-1088/pdf

Reference26 articles.

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3. A. Belafhal, H. Benzehoua and T. Usman, Certain integral transforms and their application to generate new laser waves: Exton–Gaussian beams, Adv. Math. Models Appl. 6 (2021), no. 3, 206–217.

4. A. Belafhal, S. Chib, F. Khannous and T. Usman, Evaluation of integral transforms using special functions with applications to biological tissues, Comput. Appl. Math. 40 (2021), no. 4, Paper No. 156.

5. A. Belafhal, E. M. El Halba and T. Usman, An integral transform involving the product of Bessel functions and Whittaker function and its application, Int. J. Appl. Comput. Math. 6 (2020), no. 6, Paper No. 177.

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