Analysis of New Transfer Functions by Some Integral Transforms

In this paper, we investigated the Shehu transform and the formable integral transform, both belonging to the class of Laplace-type integral transforms. The formable integral transform represents a novel and effective method for solving both ordinary and partial differential equations. We use these transforms to solve some differential equations that involve various types of derivatives, including classical, Caputo, Caputo-Fabrizio, and Atangana-Baleanu derivatives, investigating their complex dynamics and revealing the corresponding transfer functions. By extending the capabilities of Laplace and Sumudu integral transforms, these innovative integral transforms offer efficient solutions for classical as well as fractional differential equations, significantly expanding the range of solvable mathematical models. The derived transfer functions not only serve as powerful analytical tools but also demonstrate remarkable versatility in addressing diverse mathematical models, thus emphasizing their significant impact on mathematical analysis and applications.