On Fourier-Bessel matrix transforms and applications

The Fourier-Bessel transform is an integral transform and is also known as the Hankel transform. This transform is a very important tool in solving many problems in mathematical sciences, physics, and engineering. Very recently, Abdalla (AIMS Mathematics 6: [2021], 6122-6139) introduced certain Hankel integral transforms associated with functions involving generalized Bessel matrix polynomials and various applications. Motivated by this work, we introduce the Fourier-Bessel matrix transform (FBMT) containing Bessel matrix function of the first kind as a kernel. The corresponding inversion formula and several illustrative examples of this transform have been presented. A relation between the Laplace transform and the FBMT has been obtained. Furthermore, a convolution of the FBMT is constructed with some properties. In addition, some applications are proposed in the present research. Finally, we outlined the significant links for the preceding outcomes of some particular cases with our results.

Automated summary

This article introduces the Fourier-Bessel matrix transform (FBMT) and its inversion formula, explores the relationship with the Laplace transform, constructs the convolution properties of the FBMT. Some applications are proposed, and significant links between previous results of specific cases and the current results are outlined.