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

作　　者：R.K.SAXENA D.KUMAR 

机构地区：[1]Department of Mathematics and Statistics, Jai Narain Vyas University

出　　处：《Acta Mathematica Scientia》2015年第5期1095-1110,共16页数学物理学报（B辑英文版）

基　　金：NBHM Department of Atomic Energy,Government of India,Mumbai for the finanicai assistance under PDF sanction no.2/40(37)/2014/R&D-II/14131

摘　　要：The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [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, R-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, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [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, R-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, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.

关 键 词：generalized fractional calculus operators a general class of polynomials R-function H-FUNCTION /-function generalized Wright hypergeometric function Mittag-Leffler function generalized Bessel-Maitland function 

分 类 号：O172[理学—数学]