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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.
Thermal instability of a nanofluid layer under local thermal non-equilibrium
Agarwal Shilpi,Bhadauria Beer Singh 나노기술연구협의회 2015 Nano Convergence Vol.2 No.6
In this paper, we study the effect of local thermal non-equilibrium on the linear thermal instability in a horizontal layer of a Newtonian nanofluid. The nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. A two-temperature model has been used for the effect of local thermal non-equilibrium among the particle and fluid phases. The linear stability is based on normal mode technique and for nonlinear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. We observe that for linear instability, the value of Rayleigh number can be increased by a substantial amount on considering a bottom heavy suspension of nano particles. The effect of various parameters on Rayleigh number has been presented graphically. A weak nonlinear theory based on the truncated representation of Fourier series method has been used to find the concentration and the thermal Nusselt numbers. The behavior of the concentration and thermal Nusselt numbers is also investigated by solving the finite amplitude equations using a numerical method.
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 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.
Vinod Kumar Gupta,Shilpi Agarwal,Inderjeet Tyagi,Maryam Sohrabi,Ali Fakhri,Sahar Rashidi,Nima Sadeghi 한국공업화학회 2016 Journal of Industrial and Engineering Chemistry Vol.41 No.-
Carbon nanofibers have been synthesized by simple facile microwave-assisted hydrothermal route andapplied as adsorbent for the fast adsorption of methamphetamine. The topological property of CNF wasanalyzed using XRD, SEM, TEM, and nitrogen adsorption–desorption instrumental techniques. Thesignificance of the independent variables and their interactions were tested by the analysis of variance(ANOVA) and t-test statistics. Influential parameters are optimized using BBD implemented with RSM,and the optimized value of pH, adsorbent dose and temperature was found to be 8.0, 0.1 g and 298 K,respectively. Under optimal conditions, the removal efficiency of methamphetamine was found to be55.25 mg/g.
Vinod Kumar Gupta,Shilpi Agarwal,Asim Olgun,Halil I brahim Demir,Mehmet Lutfi Yola,Necip Atar 한국공업화학회 2016 Journal of Industrial and Engineering Chemistry Vol.34 No.-
In this study, the removal of cationic dyes, Basic Red 46 (BR46) and Basic Blue 41 (BB41), from aqueoussolution using boron enrichment waste (BW) and molasses modified boron enrichment waste (MBW)based nanoclays was presented in a batch system and fixed-bed column system. The effects of pH,contact time, initial solution concentration, adsorbent dosage, temperature of batch operation on theuptake of both dyes were investigated. The adsorption data were further performed on the basis ofkinetic and isotherm models. According to the results, the dye removal capacity of MBW was higher thanthat of BW. The studies demonstrated that the adsorption patterns occurred according to Langmuirisotherm model and pseudo-second-order kinetic model. The adsorption of two dyes is spontaneous andexothermic in nature. Breakthrough curves obtained from fixed-bed column tests showed that columnadsorption capacities provided strong evidence of the potential of the nanoclay for the technologicalapplications of the basic dyes removal from aqueous solutions.
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.
Omid Moradi,Vinod Kumar Gupta,Shilpi Agarwal,Inderjeet Tyagi,Mohammad Asif,Abdel Salam Hamdy Makhlouf,Hamidreza Sadegh,Ramin Shahryari-ghoshekandi 한국공업화학회 2015 Journal of Industrial and Engineering Chemistry Vol.28 No.-
Graphene (G) and Graphene oxide (GO) were employed in the present study for the removal of two toxiccationic dye Basic Red 12 (BR 12) and Basic Red 46 (BR 46), from aqueous solutions. Graphene oxide wassynthesized by Hummer–Offeman method, and then characterized by XRD (X-ray diffraction), and FT-IR(Fourier Transform Infrared spectroscopy). The influence of various physico-chemical parameters suchas electrical conductivity behaviors, contact time, solution pH, dye concentration and temperature werewell investigated and elucidated. The kinetics and thermodynamics of the toxic dye removal processwere also investigated; results clearly depicts that the kinetics of the removal of BR 12 and BR 46 using Gand GO as adsorbents follows a pseudo-second-order model. G and GO exhibited high-adsorptioncapacity for BR 12 and BR 46. The dye removal depends on the initial pH of the solution with themaximum uptake occurring at about pH 9. Moreover, the thermodynamic results confirmed thatadsorption of dye BR 46 on G and GO were exothermic and adsorption of dye BR 12 on G and GO wereendothermic in nature. The electrical conductivity behaviors of the aqueous solution were found to beenhanced by oxidation of graphene.