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Further results on fractional calculus of Saigo operators. (English) Zbl 1256.26003

Summary: The main object of the present paper is to study and develop the Saigo operators. We establish two results that give the image of the product of the multivariable \(H\)-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, the multivariable \(H\)-function and the general class of polynomials a large number of new and known images involving Riemann-Liouville and Erdélyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric functions, Mittag-Leffler functions, Whittaker functions follow as special cases of our main findings. Results given by Kilbas, Kilbas and Sebastian, Saxena et al. and Gupta et al., follow as special cases of our findings.

MSC:

26A33 Fractional derivatives and integrals
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
33C70 Other hypergeometric functions and integrals in several variables
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