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THE EXTENDED k-MITTAG-LEFFLER FUNCTION AND ITS PROPERTIES
G. Rahman,K.S. NISAR,김태균,S. MUBEEN,M. ARSHAD 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.3
In this present paper, our aim is to derive the extended k- Mittag-Leffler function by using the extended k-beta function (Mubeen et al. in J. math. anal. Volume 7 Issue 5(2016), 118-131.) and de- ne some integral representation this newly dened function. Also, we introduce the extended k-fractional derivative formula and show that the extended k-fractional derivative k-fractional of the k-Mittag-Leffler gives the extended k-Mittag-Leffler function.
Generalized fractional integration of k-Bessel function
G. Rahman,K.S. NISAR,S. MUBEEN,M. ARSHAD 장전수학회 2017 Advanced Studies in Contemporary Mathematics Vol.27 No.4
In this present paper our aim is to deal with two integral transforms which involving the Gauss hypergeometric function as its kernels. We prove some compositions formulas for such a generalized fractional integrals with k-Bessel function. The results are established in terms of generalized Wright type hypergeometric function and generalized hypergeometric series. Also, the authors presented some corresponding assertions for RiemannLiouville and ErdelyiKober fractional integral transforms.
GENERALIZED FRACTIONAL INTEGRATION OF k-BESSEL FUNCTION
G. Rahman,K.S. NISAR,S. MUBEEN,M. ARSHAD 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.3
In this present paper our aim is to deal with two integral transforms which involving the Gauss hypergeometric function as its kernels. We prove some compositions formulas for such a generalized fractional integrals with k-Bessel function. The results are established in terms of generalized Wright type hypergeometric function and gen- eralized hypergeometric series. Also, the authors presented some corre- sponding assertions for RiemannLiouville and ErdelyiKober fractional integral transforms.
INEQUALITIES INVOLVING EXTENDED k-GAMMA AND k-BETA FUNCTIONS
G. Rahman,K.S. NISAR,김태균,S. MUBEEN,M. ARSHAD 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.1
Our aim in this present paper is to introduce some inequalities such as Chebeshev's inequality, log-convexity, Holder inequality etc. which involving the extended k-gamma and k-beta function recently introduced by Mubeen et al. (J. math. anal. Volume 7 Issue 5(2016), 118-131). The obtained inequalities for extended k-beta function are the generalization of inequalities of extended beta function recently proved by Mondal (J. Inequal. Appl. (2017) 2017:10). Also, these inequalities are the extended form of the some inequalities involving k-gamma and k-beta functions earlier proved by Rehman et al. (J. Inequal. Appl., 224(1): 2014).