New intregral transform with generalized Bessel-Maitland function kernel and its applications

In this paper, authors introduce the generalized Bessel-Maitland transform whose kernel is the generalized Bessel-Maitland function. New identities are obtained for special cases of the generalized Bessel-Maitland function. Using these relations, several identities are obtained for generalized Bessel-Maitland integral transform. It is shown that some special cases of them are related with the Laplace transform and the Hankel transform. Also, some examples are given as representations of the outcomes presented here.

Automated summary

The paper introduces the generalized Bessel-Maitland transform and its kernel function, obtaining new identities for special cases. Several identities for the generalized Bessel-Maitland integral transform are derived using these relations, showing some special cases are related to the Laplace transform and the Hankel transform. Additionally, examples are provided as representations of the results presented.