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

Abstract

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.