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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.
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).
Heena Mubeen,Shankerappa S. Hatti 국립중앙과학관 2018 Journal of Asia-Pacific Biodiversity Vol.11 No.4
Earthworm survey was conducted in the selected habitats of Koppal district (15°09′00″ to 16°03′30″) of Hyderabad- Karnataka region. Earthworms were collected from Holemudalapura, Matti Mudalapura, Shivapur, Nelogal, Taralkatti, Putakmari, Kurubanhal, Budakunti, Anegundi and Rampur. 8 genera and 14 species of earthworms were identified viz., Dichogaster bolaui, Dichogaster modigliani, Octochaetona albida, Octochaetona paliensis, Octochaetona parva and Octochaetona prashadi belonging to family OCTOCHAETIDAE; Lampito mauritii, Perionyx fulvus, Perionyx koboensis, Perionyx millardi, Polypheretima elongata thecomorph and Polypheretima elongata athecomorph belonging to family MEGASCOLICIDAE; Thatonia gracilis and Thatonia parva belonging to family OCNERODRILIDAE and Eudrilus eugeniae belonging to family EUDRILIDAE. The smallest being Thatonia gracilis having a length of 2–2.5 cm and diameter of 1–1.5 mm and largest being Eudrilus euginiae having length 26–27 cm and diameter 5–5.6 mm. Dichogaster bolaui, Lampito mauritii, Perionyx koboensis Perionyx millardi, Thatonia gracilis & Thatonia parva were found in the garbage. Dichogaster modigliani, Lampito mauritii, Octochaetona albida, Octochaetona paliensis, Octochaetona parva, Polypheretima elongata thecomorph were found near the bore-well sewage water. Eudrilus eugeniae, Perionyx millardi, Polyperetima elongata athecomorph, Thatonia parva and Octochaetona prashadi in the gutter. Perionyx koboensis was found in the irrigated land. Parameters like temperature, humidity were recorded and physicochemical analysis of the soil was carried out.
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.
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.