Abstract
In this paper, we establish modified Saigo fractional integral operators involving the product of a general class of multivariable polynomials and the multivariable H-function. The results established here are of general nature and provide extension of some results obtained recently by Saxena et al.
Highlights
Introduction and preliminaries The multivariableH-function is defined and studied by Srivastava and Panda ([1], p. 271, Eq (4.1)) in terms of Mellin–Barnes type contour integral as follows: ⎡ H [z1, zr ] =Hp0,qn::pm11,q,n11;.;....;.p;mr,qr,rnr ⎢⎢⎣ z1 ...zr (aj; αj, . . . , αj(r))1,p : (bj; βj, . . . , βj(r))1,q : ⎤(cj, γj )1,p11,q1
Where (α ) > 0, and α,β n stands for the generalized polynomial set defined by the following Rodrigues type formula ([20], p. 64, Eq (2.18)): α,β,τ n
We derived analogous results in the form of Riemann–Liouville and Weyl fractional integral operators, which have been depicted in corollaries
Summary
686, Eq (1.4)) gave the definition of multivariable generalization of the polynomials Snm(x) as follows: h1 k1 +···+hs ks ≤L Choosing constants to be real or complex, as Srivastava [12] defined by s = 1 on the above polynomial, we obtain a polynomial of the form Snm(x). For the operators I0α,x,,βθ ,η and Jxα,∞,β,θ,η there holds interesting results similar to the ones derived in a series of earlier papers [13,14,15,16,17,18,19].
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