GENERALIZED FRACTIONAL CALCULUS OF THE ALEPH-FUNCTION INVOLVING A GENERAL CLASS OF POLYNOMIALS

The object of this article is to study and develop the generalized fractional calculus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of aleph-function, Appell function F-3 and a general class of polynomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Crag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, aleph-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, I-function, Mittag-Leffler function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.