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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).
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.
( N. Menaria ),( R. K. Parmar ),( S. D. Purohit ),( K. S. Nisar ) 호남수학회 2017 호남수학학술지 Vol.39 No.3
By means of the Oberhettinger integral, certain generalized integral formulae involving product of generalized k-Bessel function w (z) and general class of polynomials S [x] are derived, the results of which are expressed in terms of the generalized Wright hypergeometric functions. Several new results are also obtained from the integrals presented in this paper.
Menaria, N.,Parmar, R.K.,Purohit, S.D.,Nisar, K.S. The Honam Mathematical Society 2017 호남수학학술지 Vol.39 No.3
By means of the Oberhettinger integral, certain generalized integral formulae involving product of generalized k-Bessel function $w^{{\gamma},{\alpha}}_{k,v,b,c}(z)$ and general class of polynomials $S^m_n[x]$ are derived, the results of which are expressed in terms of the generalized Wright hypergeometric functions. Several new results are also obtained from the integrals presented in this paper.
THE (k, s)-FRACTIONAL CALCULUS OF CLASS OF A FUNCTION
( G. Rahman ),( A. Ghaffar ),( K. S. Nisar ),( Azeema ) 호남수학회 2018 호남수학학술지 Vol.40 No.1
In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional inte-gral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.
THE (k, s)-FRACTIONAL CALCULUS OF CLASS OF A FUNCTION
Rahman, G.,Ghaffar, A.,Nisar, K.S.,Azeema, Azeema The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.1
In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.
Search for the rare decayD0→γγat Belle
Nisar, N. K.,Mohanty, G. B.,Trabelsi, K.,Aziz, T.,Abdesselam, A.,Adachi, I.,Aihara, H.,Asner, D. M.,Aulchenko, V.,Aushev, T.,Ayad, R.,Babu, V.,Badhrees, I.,Bahinipati, S.,Barberio, E.,Behera, P.,Bhard American Physical Society 2016 Physical Review D Vol.93 No.5
<P>We search for the rare radiative decay D-0 -> gamma gamma using a data sample with an integrated luminosity of 832 fb(-1) recorded by the Belle detector at the KEKB e(+)e(-) asymmetric-energy collider. We find no statistically significant signal and set an upper limit on the branching fraction of B(D-0 -> gamma gamma) < 8.5 x 10(-7) at 90% confidence level. This is the most restrictive limit on the decay channel to date.</P>
SOME UNIFIED INTEGRALS ASSOCIATED WITH THE GENERALIZED STRUVE FUNCTION
K.S. NISAR,D.L. SUTHAR,S.D. Purohit,M. ALDHALFALLAH 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.2
This paper is devoted for the study of a new generalization of Struve type function. In this paper, we establish four new integral formulas involving the Galue type Struve function, which are express in term of the generalized (Wright) hypergeometric functions. The result established here are general in nature and are likely to nd useful in applied problem of sciences, engineering and technology.