H-Function in Science and Engineering

Abstract

This chapter deals with integrals involving H-functions. We propose to present the results for Mellin, Laplace, Hankel, Bessel, and Euler transforms of the H-functions. Further, on account of the importance and considerable popularity achieved by fractional calculus, that is, the calculus of fractional integrals and fractional derivatives of arbitrary real or complex orders, during the last four decades due to its applications in various fields of science and engineering, such as fluid flow rheology, diffusive transport akin to diffusion, electric networks and probability, the discussion of H-function is more relevant. In this connection, one can refer to the work of Phillips (1989, 1990), Bagley (1990), Bagley and Torvik (1986) and Somorjai and Bishop (1970) and the book by Podlubny (1999). In the present book, fractional integration and fractional differentiation of the H-functions will be discussed. A long list of papers on integrals of the H-functions is available from the bibliography of the books by Mathai and Saxena (1978), Srivastava et al. (1982), Prudnikov et al. (1990) and Kilbas and Saigo (2004).