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-fun...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.展开更多
In order to study discrete fractional Birkhoff equations for Birkhoffian systems,the method of isochronous variational principle is used in this paper. Discrete fractional Pfaff-Birkhoff principle in terms of time sca...In order to study discrete fractional Birkhoff equations for Birkhoffian systems,the method of isochronous variational principle is used in this paper. Discrete fractional Pfaff-Birkhoff principle in terms of time scales is presented. Discrete fractional Birkhoff equations with left and right discrete operators of Riemann-Liouville type are established and some special cases including classical discrete Birkhoff equations,discrete fractional Hamilton equations and discrete fractional Lagrange equations are discussed. Finally,an example is devoted to illustrate the results.展开更多
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
文摘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.
基金National Natural Science Foundations of China(Nos.11272227,11572212)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province,China(No.KYLX15_0405)
文摘In order to study discrete fractional Birkhoff equations for Birkhoffian systems,the method of isochronous variational principle is used in this paper. Discrete fractional Pfaff-Birkhoff principle in terms of time scales is presented. Discrete fractional Birkhoff equations with left and right discrete operators of Riemann-Liouville type are established and some special cases including classical discrete Birkhoff equations,discrete fractional Hamilton equations and discrete fractional Lagrange equations are discussed. Finally,an example is devoted to illustrate the results.
