Theory and applications on a new generalized Laplace-type integral transform

In this paper, several theorems and relations are examined by using a generalized Laplace-type integral transform. A generalization of the harmonic oscillator in a non-resisting and resisting medium problems, initial-boundary problems, and integral equations is solved via this integral transform. Furthermore, the well-known series entitled as Basel problem is obtained in a similar way. Moreover, we compare numerically classical and newly introduced by us integral transform.

Automated summary

In this paper, various theorems and relationships are examined using a generalized Laplace-type integral transform. The harmonic oscillator, initial-boundary problems, and integral equations in non-resisting and resisting mediums are solved through this integral transform. Additionally, the well-known Basel problem series is obtained using a similar approach. Moreover, a numerical comparison between the classical and newly introduced integral transforms is conducted.