Abstract
Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols and , we introduce here the family of the incomplete generalized -hypergeometric functions and . The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second -Appell hypergeometric functions and of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.
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