On Weyl fractional integral operators

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Rashmi Jain
M. A. Pathan


In this paper, we first establish an interesting theorem exhibiting a relationship existing between the Laplace transform and Weyl fractional integral operator of related functions. This theorem is sufficiently general in nature as it contains $n$ series involving arbitrary complex numbers $ \Omega(r_1,\ldots r_n) $. We have obtained here as applications of the theorem, the Weyl fractional integral operators of Kamp'e de F'eriet function, Appell's functions $ F_1 $, $ F_4 $, Humbert's function $ \Psi_1$ and Lauricella's, triple hypergeometric series $ F_E $. References of known results which follow as special cases of our theorem are also cited. Finally, we obtain some transformations of $ F^{(3)}$ and Kamp'e de F'eriet function with the application of our main theorem .

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How to Cite
Jain, R., & Pathan, M. A. (2004). On Weyl fractional integral operators. Tamkang Journal of Mathematics, 35(2), 169–174. https://doi.org/10.5556/j.tkjm.35.2004.218
Author Biographies

Rashmi Jain

Department of Mathematics, M. R. Engineering College, Jaipur, (Rajasthan), India.

M. A. Pathan

Department of Mathematics, Aligarh Muslim University, Aligarh-202002, (U.P.), India.