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Recently, an extended operator of fractional derivative related to a generalized Beta function was used in order to obtain some generating relations involving the extended hypergeometric functions . The main object of this paper is to present a further generalization of the extended fractional derivative operator and apply the generalized extended… (More)
The main object of this paper is to present generalization of extended beta function, extended hypergeometric and con-fluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function , Mellin transform, beta distribution, differentiation formulas, transform formulas, recurrence… (More)
–– Recently an extension of beta function is defined by introducing an extra parameter is proved to be useful earlier (Aslam Chaudhry 1997  and A. R. Miller 1998 ). In this research note, we generalize the incomplete beta function and obtained the various integral representations and properties. Furthermore, we obtained the beta distribution for… (More)
In this paper, we aim at establishing two generalized integral formulae involving generalized Mittag-Leffler function which are expressed in terms of the generalized hypergeometric function and generalized (Wright) hypergeometric function. Some interesting special cases of our main results are also considered. The results are derived with the help of an… (More)
A general strategy for the synthesis of enantiomerically pure 4-substituted [2.2]paracyclophanes from a common sulfoxide precursor is described.