Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지

A Study of Modified H-transform and Fractional Integral Operator

  • Gupta, Kantesh (Department of Mathematics, Malviya National Institute of Technology)
  • Received : 2006.03.31
  • Published : 2007.12.23
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we establish a theorem wherein we have obtained the image of modified H-transform under the fractional integral operator involving Foxs H-function. Three corollaries of this theorem have also been derived. Further, we obtain one interesting integral by the application of the third corollary. The importance of above findings lies in the fact that our main theorem involves Fox H-function which is very general in nature. The result obtained earlier by Tariq (1998) is a special case of our main findings.

Keywords

References

  1. C. Fox , The G and H-functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc., 98(1961), 395-429.
  2. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, 1963.
  3. A. M. Mathai and R. K. Saxena, The H-Functions with Applications in Statistics and other Disciplines, John Wiley and Sons, 1974.
  4. P. K. Mittal and K. C. Gupta, An integral involving generalized function of two variables, Proc. Indian Acad. Sci. Sect. A., 75(1972), 117-123.
  5. M. Saigo, R. K. Saxena and J. Ram, On the two dimensional generalized Weyl fractional calculus associated with two dimensional H-transform, J. Fractional Calculus, 8(1995), 63-73.
  6. R. K. Saxena and R. K. Kumbhat, Integral operators involving H-functions, Indian J. Pure Appl. Maths., 5(1974), 1-6.