This study introduces a novel and more generalized form of the fractionalized kinetic equation (KE), expressed using the incomplete H-function combined with an exponential function. The significance of the fractional KE, which plays a crucial role in various engineering and scientific applications, is analyzed through the of incomplete special functions, including the incomplete H-function, H-function, Fox-Wright function, and Meijer’s G-function. Solutions are efficiently derived using the modified degenerate Laplace transform, which incorporates these incomplete special functions. Additionally, graphical simulations are presented to illustrate the results. The obtained conclusions are broad in scope, providing a framework for generating solutions to a wide range of fractional kinetic equations.