Yücef A.Tan N.2024-08-042024-08-0420172164-6457https://doi.org/10.5890/JAND.2017.06.013https://hdl.handle.net/11616/91944There is considerable interest in the study of fractional order deriva- tive/integrator but obtaining analytical impulse and step responses is a difficult problem. Therefore all methods reported on to date use approximations for the fractional derivative/integrator both for an- alytical based computations and more relevantly in simulation stud- ies. In this paper, an analytical formula is first derived for the in- verse Laplace transform of fractional order integrator, 1/s? where ? ? R and 0 < ? <1 using Stirling's formula and Gamma func- tion. Then, the analytical step response of fractional integrator has been computed from the derived impulse response of 1/s?. The ob- tained analytical formulas for impulse and step responses of frac- tional order integrator are exact results except the very small error due to the neglected terms of Stirling's series. The results are com- pared with some well known integer order approximation methods and Grunwald-Letnikov (GL) approximation technique. It has been shown via numerical examples that the presented method is very suc- cessful according to other methods. © 2017 L&H Scientific Publishing, LLC.eninfo:eu-repo/semantics/closedAccessConvolution integralFractional order integratorGamma functionLaplace transformStirling's formulaArticle6230331410.5890/JAND.2017.06.0132-s2.0-85020888299Q4