Inverse Laplace Transform of the Incomplete H-Function

Abstract

Special functions have enormous applications in theoretical and applied mathematics. This field is constantly expanding and addressing new problems in engineering applications and applied sciences. H-function one and more variables have been applied in large range of areas, such as electronics and communication, astrophysics, fractional differential equations, super statistics, diffusion, reaction–diffusion, and other fields like probability theory, biology, and theoretical physics. Some situations of heat conduction and astrophysics problems are not adequately addressed by basic category of special functions. To address such problems, incomplete special functions found the way in the literature. Incomplete H-functions are attracting researchers working on heat conduction and astrophysics problems. The paper aims to transform the products of algebraic powers and incomplete H-function in another domain using inverse laplace transform. Results are obtained in terms of the incomplete H-function as compact form. Further, some particular cases are mentioned by giving special values to the incomplete H-function’s parameters.