ABSTRACT
In recent years, there has been a lot of interest in the special functions of extended functions and their uses, some of which define the totality of partial analyses, provide useful tools for describing natural phenomena, and are thus more suitable for describing some applicable models. This work illustrates some of the rich theoretical and applied behaviors found in models of special functions, especially expansion-generalized gamma delta, and approaches to generalizing integrals and derivatives more comprehensively, through the weights provided by extended gamma functions. The researcher tried to link all the basic modifications that were obtained previously, and with a summary of the modifications that appeared on the most important special functions related to the extended generalized gamma function and the special functions overlapping with it related to the fractional calculus and more results about the generalized gamma function that occur in the diffraction theory, and some special functions related to fractional functions. Calculus and more results about the extended gamma function that occurs in diffraction theory that occurs in diffraction theory in most applications with full control over diffraction access to functions (of different scale) diffraction of light waves, in traditional diffraction theory.
Keywords: Extended, Gamma functions, Transformation functions, Fractional calculus, and Control theory.
Citation: Lahcene B, Al Mamun AM, Hossain MR, and Islam S. (2022). Theoretical results of the extended Gamma function and its applications, Int. J. Mat. Math. Sci., 4(3), 61-74.
https://doi.org/10.34104/ijmms.022.061074
