Estimation of a modified integral associated with a special function kernel of Fox's $H$-function type
Commun. Korean Math. Soc. 2020 Vol. 35, No. 1, 125-136
https://doi.org/10.4134/CKMS.c180410
Published online January 31, 2020
Shrideh Khalaf Qasem Al-Omari
Al-Balqa Applied University
Abstract : In this article, we discuss classes of generalized functions for certain modified integral operator of Bessel-type involving Fox's $H$-function kernel. We employ a known differentiation formula of Fox's $H$-function to obtain the definition and properties of the distributional modified Bessel-type integral. Further, we derive a smoothness theorem for its kernel in a complete countably multi-normed space. On the other hand, using an appropriate class of convolution products, we derive axioms and establish spaces of modified Boehmians which are generalized distributions. On the defined spaces, we introduce addition, convolution, differentiation and scalar multiplication and further properties of the extended integral.
Keywords : Fox's $H$-function, Bessel-type integral, Boehmians, generalized functions, distribution
MSC numbers : 46F12, 46T30
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