International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue XII, December 2017 | ISSN 2321–2705  

Some Results Conncered to the I-Function of Fractional Calculus

V. S. Dhakar[1] and Smita Sharma[2]
[1, 2]Department of Mathematics, ITM Group of Institutions Gwalior, Gwalior-474001, INDIA

Abstract:- The main objects of this paper is to derive the results for the I- function involving the Riemann-Liouville, the Weyl and such other fractional calculus operators as those based on the Cauchy- Goursat integral formula. The results derived in this paper are basic in nature and may include a number of known and new results as special cases.

Keyward: – Riemann-Liouville, the Weyl Oprators, H-function, G-function, and I function

I. INTRODUCTION AND PRELIMINARIES

In view of the generality of the I-function, on specializing the various parameters, we can obtain from our results, several results involving a remarkably wide variety of useful functions, which are expressible in terms of H-function, Gfunction, Fox’s Wright function, generalized mittag-Leffler functions and their various special cases. Thus, the results presented in this paper would at once yield a very large number of results involving a large variety of special functions occurring in the problems of science, engineering, mathematical physics etc. In 1961, Charles Fox [3] introduced a function which is more general in than the Meijer’s G-function and this function is well known in the literature of special functions as Fox’s Hfunction.

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