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agarwal,Shilpi Jain,김용섭 경남대학교 수학교육과 2018 Nonlinear Functional Analysis and Applications Vol.23 No.4
Authors established some (presumably) new fractional integral and Beta trans- form formulas for the generalized extended Appell’s and Lauricella’s hypergeometric func- tions which have recently been introduced by Kim.
CERTAIN INTEGRAL FORMULAS ASSOCIATED WITH ALEPH (ℵ)-FUNCTION
Agarwal, Praveen,Jain, Shilpi,Karimov, Erkinjon T.,Prajapati, Jyotindra C. Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.2
Recently many authors have investigated so-called Aleph (${\aleph}$)-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph (${\aleph}$)-function. Precisely, integrals with product of Aleph (${\aleph}$)-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.
ON SOME FORMULAS FOR THE GENERALIZED APPELL TYPE FUNCTIONS
Agarwal, Praveen,Jain, Shilpi,Khan, Mumtaz Ahmad,Nisar, Kottakkaran Sooppy Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.4
A remarkably large number of special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) have been investigated by many authors. Motivated the works of both works of both Burchnall and Chaundy and Chaundy and very recently, Brychkov and Saad gave interesting generalizations of Appell type functions. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present some new differential formulas for the generalized Appell's type functions ${\kappa}_i$, $i=1,2,{\ldots},18$ by considering the product of two $_4F_3$ functions.
Image formulas and graphical interpretation of fractional derivatives of R-function and G-function
Mehar Chand,Praveen Agarwal,Shilpi Jain,Guotao Wang,K.S. NISAR 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.4
In this paper, our main objective is to establish certain new image formulas of R- and G-functions by applying the operators of fractional derivative involving Appell's function F3(.) due to Saigo-Maeda and the main results interpreted graphically by implementing the MatLab(R2012a). Furthermore, by employing some integral transforms on the resulting formulas, we presented some more image formulas. All the results derived here are of general character and can yield a number of (known and new) results in the theory of special functions.
EXTENDED HYPERGEOMETRIC FUNCTIONS OF TWO AND THREE VARIABLES
AGARWAL, PRAVEEN,CHOI, JUNESANG,JAIN, SHILPI Korean Mathematical Society 2015 대한수학회논문집 Vol.30 No.4
Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions $_pF_q$ have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and $_pF_q$ have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function $B_p^{({\alpha},{\beta};m)}$ (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.
CERTAIN INTEGRALS ASSOCIATED WITH GENERALIZED MITTAG-LEFFLER FUNCTION
Agarwal, Praveen,Choi, Junesang,Jain, Shilpi,Rashidi, Mohammad Mehdi Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.1
The main objective of this paper is to establish certain unified integral formula involving the product of the generalized Mittag-Leffler type function $E^{({\gamma}_j),(l_j)}_{({\rho}_j),{\lambda}}[z_1,{\ldots},z_r]$ and the Srivastava's polynomials $S^m_n[x]$. We also show how the main result here is general by demonstrating some interesting special cases.
Certain inequalities for series involving the generalized hypergeometric function 2F2
최준상,S. S. Dragomir,Praveen Agarwal,Shilpi Jain 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.2
The objective of this paper is to establish certain inequal- ities for series involving the generalized hypergeometric function 2F2 with the help of some known inequalities for 2F1 introduced by Koti [4]. Among a large number of possible special cases of our main results, only one special case is considered.
Jangra Sumit,Dhall Heena,Aggarwal Shilpi,Mandal Bikash,Jain Rakesh Kumar,Ghosh Amalendu 한국응용곤충학회 2020 Journal of Asia-Pacific Entomology Vol.23 No.2
Thrips palmi is an important insect pest of vegetables and ornamental crops worldwide. Besides direct damage caused by feeding, it transmits several tospoviruses in a persistent-propagative manner. Eggs of T. palmi are microscopic and embedded within plant tissue by the sharp ovipositor of adult female. In the present study, an artificial oviposition setup has been standardized for T. palmi. Eggs of T. palmi were harvested in sterile water between two thin membranes. The developmental stages of T. palmi embryo were studied starting from oviposition up to hatching by inverted and confocal reflection microscopy. Energids were homogeneously distributed at an early stage of development. The anterior end of the egg curved with a constriction post 38 h. Initiation of tissue organization, mouthparts, appendages, compound eyes were observed at different time points. Appendages were well developed and segmentation was prominent post 70 h. The embryo was completely developed at around 80 h and hatched by 86 h post oviposition at 28 °C temperature. The study first time reports the embryonic development of T. palmi that would be helpful in detailed investigations of thrips developmental biology and evolution.