Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Some Theorems Connecting the Unified Fractional Integral Operators and the Laplace Transform

  • Soni, R. C. (Department of Mathematics, M. N. Institute of Technology) ;
  • Singh, Deepika (Department of Mathematics, M. N. Institute of Technology)
  • Received : 2002.04.19
  • Published : 2005.06.23
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Abstract

In the present paper, we obtain two Theorems connecting the unified fractional integral operators and the Laplace transform. Due to the presence of a general class of polynomials, the multivariable H-function and general functions ${\theta}$ and ${\phi}$ in the kernels of our operators, a large number of (new and known) interesting results involving simpler polynomials (which are special cases of a general class of polynomials) and special functions involving one or more variables (which are particular cases of the multivariable H-function) obtained by several authors and hitherto lying scattered in the literature follow as special cases of our findings. Thus the Theorems obtained by Srivastava et al. [9] follow as simple special cases of our findings.

Keywords

References

  1. Trans. Amer. Math. Soc. v.98 The G and H functions as symmetrical Fourier kernels Fox, C.
  2. Proc. Indian Acad. Sci. (Math. Sci.) v.104 On composition of some general fractional integral operators Gupta, K.C.;Soni, R.C.
  3. Proc. Indian Acad. Sci. (Math. Sci) v.106 On unified fractional integral operators Gupta, K.C.;Soni, R.C.
  4. The H-function with applications in statistics and other disciplines Mathai, A.M.;Saxena, R.K.
  5. Indian J. Math. v.14 A contour integral involving Fox's H-function Srivastava, H.M.
  6. The H-functions of one and two variables with applications Srivastava, H.M.;Gupta, K.C.;Goyal, S.P.
  7. Univalent functions, fractional calculus and their applications Srivastava, H.M.;Owa, S.(eds.)
  8. J. Reine Angew. Math. v.283/284 Some Bilateral generating functions for a class of generalized hypergeometric polynomials Srivastava, H.M.;Panda, R.
  9. J. Math. Anal. Appl. v.172 Some existence and connection Theorems associated with the Laplace transform and a certain class of integral operators Srivastava, H.M.;Saigo, M.;Raina, R.K.
  10. Rend. Circ. Mat. Palermo v.32 The integration of certain products of the multivariable H -function with a general class of polynomials Srivastava, H.M.;Singh, N.P.