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Kumar D.,Jagan Nath Gupta Institute of Engineering and Technology | Singh J.,Jagan Nath University | Sushila,Jagan Nath University
Romanian Reports in Physics | Year: 2013

In this paper, we present an algorithm of the homotopy analysis transform method (HATM) which is a combination of Laplace transform method and the homotopy analysis method (HAM) to solve generalized biological population models. The fractional derivatives are described by Caputo sense. The proposed method presents a procedure of constructing the set of base functions and gives the high-order deformation equations in a simple form. The proposed scheme provides the solution in the form of a rapidly convergent series. Three examples are used to illustrate the preciseness and effectiveness of the proposed method. The results show that the HATM is very efficient, simple and can be applied to other nonlinear problems.

Gupta S.,Jagan Nath Gupta Institute of Engineering and Technology | Kumar D.,University of Rajasthan | Singh J.,Jagan Nath University
Alexandria Engineering Journal | Year: 2015

The aim of this paper was to present a user friendly numerical algorithm based on homotopy perturbation transform method for solving various linear and nonlinear convection-diffusion problems arising in physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. The homotopy perturbation transform method is a combined form of the homotopy perturbation method and Laplace transform method. The nonlinear terms can be easily obtained by the use of He's polynomials. The technique presents an accurate methodology to solve many types of partial differential equations The approximate solutions obtained by proposed scheme in a wide range of the problem's domain were compared with those results obtained from the actual solutions. The comparison shows a precise agreement between the results. © 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.

Vyas R.,Jaipur National University | Vyas R.,Malaviya National Institute of Technology, Jaipur | Kumar P.,National Physical Laboratory India | Dwivedi J.,National Physical Laboratory India | And 8 more authors.
RSC Advances | Year: 2014

Herein, we demonstrate the growth of Fe-doped ZnO nanowires using a typical vapour phase transport process for oxygen gas sensing application. The morphologies of these nanowires have been evaluated by high-resolution transmission electron microscopy, which confirms the formation of ZnO nanowires with 20-50 nm diameter and with a d-spacing of ∼0.270 nm, corresponding to (002) planes. The energy dispersive X-ray spectroscopy result reveals the presence of Fe, Zn and O elements in 9 wt% Fe-doped ZnO nanowires. The Raman and photoluminescence spectroscopy results explore the oxygen deficient structure of these nanowires with Fe ion occupying tetrahedral sites in the ZnO lattice along with some interstitial Zn and Fe ions. Furthermore, these nanowires arrays illustrate a sensitivity of 23 and 31 with fast response/recovery times of about 38 s/46 s and 11 s/11 s at an operating temperatures of 100 °C and 140°C, respectively. The obtained results established that these luminescent ZnO nanowires could be an excellent choice for high-performance oxygen gas sensing application. © 2014 The Royal Society of Chemistry.

Sharma V.,Jagan Nath Gupta Institute of Engineering and Technology | Sagar P.,Kumaun University | Rohit,Kumaun University
Journal of the Indian Chemical Society | Year: 2012

Pd II complexes of azobenzene and anthranilic acid were found most efficient towards the catalytic oxidation of internal alkenes, aromatic hydrocarbons and alcohol in DMF-C 2H 5OH (6 : 4) mixed solvent system both under normal and high pressure of molecular oxygen. No diminished catalytic activity was observed even after 6-8 repeated catalytic runs. Effect of extra ligand on the rate of oxidation, nature and percentage yield of products was investigated.

Kumar S.,National Institute of Technology Jamshedpur | Singh J.,Jagan Nath University | Kumar D.,Jagan Nath Gupta Institute of Engineering and Technology
Ain Shams Engineering Journal | Year: 2014

The main aim of the present work is to propose a new and simple algorithm for Volterra integral equation arising in demography, the study of viscoelastic materials, and in insurance mathematics through the renewal equation by using homotopy analysis transform method. The homotopy analysis transform method is an innovative adjustment in Laplace transform algorithm and makes the calculation much simpler. The solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. The beauty of the paper is coupling of two techniques. Finally, two numerical examples are given to show the accuracy and stability of this method. © 2013 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

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