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Applied Math Research

Praveen Kumar Gupta (P. K. Gupta)

PKG

Designation: Research Scholar

Phone: +91-9453555044

e-mail: pkguptaitbhu@hotmail.com; praveen.rs.apm@itbhu.ac.in

Research Areas: Mathematical Modelling, Heat Transfer, Fractional Calculus, Nonlinear Dynamics, Numerical Methods, Approximate Analytical Methods,

Ph.D. Thesis title: "Some studies on Mathematical Modelling of Heat transfer in Biological Tissues"

Biography:

M. Sc.(Mathematics) and Ph. D. (Submitted on February 15, 2011).

Research Experience : Doctoral ( July 2007 to till date )
Publications : 27 (International Journals)

Paper Presentation in International and National Conferences/Workshops:

  1. A fractional predator-prey model and its solution presented in the Application of mathematical methods in physical problems (AMMPP-2009) held at Department of Mathematics, Sikkim Manipal Institute of Technology, Majitar, East-Sikkim, during December 18-23, 2009.
  2. Application of He’s Homotopy Perturbation Method to Fractional Diffusion equations presented in the National Conference on "Recent Trends in Mathematical Sciences(RTMS-2010) held at Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi, India, during March 18-20, 2010.
  3. Approximate Analytical solution of Fractional Lotka-Volterra Equation presented in the International Congress of Mathematicians (ICM-2010) held at Hyderabad International Conventional Center, Hyderabad, India, during August 19 - 27, 2010.

International/National attended Conferences/Workshops/Short term courses/Training Programs:

  1. National Conference & Workshop on High Performance Computing & Applications (HPCA-2008) held at Department of Computer Science, Banaras Hindu University, Varanasi, India, during February 25-27, 2008.
  2. Short term course on Computer Programming using C  held at Computer Centre of the Banaras Hindu University, Varanasi, India, during September 1-6, 2008.
  3. Indo-German Workshop-cum-lecture series on Computational Models and Methods Driven by Industrial Problems in Phase-II held at IIT Madras, Chennai, India, during January 5-16, 2009.
  4. Short term course on Energy Conversion & Management  held at Malaviya Centre for Innovation, Incubation & Entrepreneurship, I.T.B.H.U. Varanasi, India, during April 03-09, 2009.
  5. 2nd INUP Workshop on Nanofabrication Technologies  held at IIT Bombay, Mumbai, India, during May 30-31, 2009.
  6. 2nd IEEE International Workshop on Electron Devices and Semiconductor Technology  (IEDST-2009) held at IIT Bombay, Mumbai, India, during June 1-2, 2009.
  7. National Workshop-Cum-Training Program on Advanced Numerical Techniques and Applications  (NWCTP-ANTA) held at Department of Mathematics, Banaras Hindu University, Varanasi, India, during June 29 - July 11, 2009.
  8. Training program on LATEX and other Open Source Software held at D.S.T. Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, India, during December 7 - 12, 2009.

Reviewer of the International Journals:

1.  Acta Mathematica Sinica
2.  International Journal for Numerical Methods in Fluids
3.  International Journal of Computational Methods
4.  International Journal of Physical Sciences
5.  Computer and Mathematics with Applications
6.  Zeitschrift-fuer-Naturforschung A

 

Publications:

Heat transfer

1.      Praveen Kumar Gupta (with Jitendra Singh and Kabindra Nath Rai), Numerical Simulation for Heat Transfer in tissues during Thermal therapy, Journal of Thermal Biology, Volume 35, Issue 6, pp. 295-301, 2010 (Elsevier) (Impact Factor: 1.305).

2.      Praveen Kumar Gupta (with Jitendra Singh and Kabindra Nath Rai), Homotopy perturbation Method to space-time fractional solidification in a finite slab, Applied Mathematical Modelling, Volume 35, Issue 4, pp. 1937-1945, 2011 (Elsevier) (Impact Factor: 1.375).

3.      Praveen Kumar Gupta (with Jitendra Singh and Kabindra Nath Rai), Variational iteration method to solve moving Boundary problem with temperature dependent Physical properties, Thermal Sciences, DOI: 10.2298/TSCI100226024S, In Press (2011) (Vinča Institute of Nuclear Sciences) (Impact Factor: 0.620).

 

Dynamical system

4.      Praveen Kumar Gupta (with Subir Das and Rajeev), A Fractional predator-prey Model and its Solution, International Journal of Nonlinear Sciences and Numerical Simulation, Volume 10, Issue 7, pp. 873-876 (2009) (Freund Pub. House Ltd.) (Impact Factor: 5.276).

5.      Praveen Kumar Gupta (with Subir Das), A mathematical model on fractional Lotka-Volterra equations, Journal of Theoretical Biology, Volume 277, Issue 1, pp. 1-6 (2011) (Elsevier) (Impact Factor: 2.574).

6.      Praveen Kumar Gupta (with Subir Das and Kumar Vishal), Approximate approach to the Das Model of Fractional Logistic Population Growth, Applications & Applied Mathematics, Volume 5, Issue 10, pp. 1702-1708 (December 2010) (Prairie View A&M University, USA).

7.      Praveen Kumar Gupta (with Subir Das and Hossein Jafari), Approximate analytical solution of the Fractional predator-prey model for n - species by Homotopy Analysis Method, Journal of Advanced Research in Scientific Computing, Accepted (2011) (Institute of Advanced Scientific Research).

 

Fractional Diffusion equation

8.      Praveen Kumar Gupta (with Subir Das, Vinod Shankar Pandey and Kabindra Nath Rai), Application of He’s Homotopy Perturbation Method to Fractional Diffusion Equations,  Zeitschrift für Natur-forschung, Volume 65a, Issue1, pp. 53-58 (2010) (Verlag-der-Zeitschrift-für-Naturforschung) (Impact Factor: 0.850).

9.      Praveen Kumar Gupta (with Subir Das), An Approximate Analytical Solution of the Fractional Diffusion Equation with Absorbent Term and External Force by Homotopy Perturbation Method, Zeitschrift für Naturforschung, Volume 65a, Issue 3, pp. 182-190 (2010) (Verlag-der-Zeitschrift-für-Naturforschung) (Impact Factor: 0.850).

10.  Praveen Kumar Gupta (with Subir Das and Rajnesh Kumar), Homotopy Analysis Method for Fractional Diffusion Equation with Absorbent Term and External Force, Journal of Nonlinear Systems and Applications, Volume 1, Issue 3, pp. 141-145 (2010).

11.  Praveen Kumar Gupta (with Subir Das and Rajnesh Kumar), An approximate analytical solution of the fractional diffusion equation with external force and different type of absorbent term - Revisited, Applications & Applied Mathematics, Special Issue No. 1, pp. 101-109 (August 2010) (Prairie View A&M University, USA).

12.  Praveen Kumar Gupta (with Subir Das and Rajnesh Kumar), The homotopy analysis method for fractional Cauchy reaction-diffusion problems, International Journal of Chemical Reactor Engineering, Volume 9, A15 (2011) (Impact Factor: 0.733).

13.  Praveen Kumar Gupta (with Subir Das), Approximate analytical solutions of time-space fractional diffusion equation by Adomian Decomposition Method and Homotopy Perturbation Method, Special Issue of Analele Stiintifice-ale-Universitatii Ovidius, Seria Matematica, Accepted (2010) (Ovidius University, Constanta, Romania).

14.  Praveen Kumar Gupta (with Subir Das and Rajnesh Kumar), Analytical approximate solutions of space-and time- fractional diffusion equation with a moving boundary condition, Zeitschrift für Naturforschung A, Volume 66a, Issue 5, pp. 281-288 (2011) (Verlag-der-Zeitschrift-für-Naturforschung) (Impact Factor: 0.850).

15.  Praveen Kumar Gupta (Subir Das and Kumar Vishal), Solution of the nonlinear fractional diffusion equation with absorbent term and external force, Applied Mathematical Modelling, Volume 35, Issue 8, pp. 3970-3979 (2011) (Elsevier) (Impact Factor: 1.375).

16.  Praveen Kumar Gupta (with Subir Das and Pradyumna Ghosh), An approximate solution of nonlinear fractional reaction-diffusion equation, Applied Mathematical Modelling, Volume 35, Issue 8, pp. 4071-4076 (2011) (Elsevier) (Impact Factor: 1.375).

 

Mathematical modeling using fractional calculus

17.  Praveen Kumar Gupta (with Mithilesh Singh), Homotopy perturbation method for fractional Fornberg-Whitham equation, Computer and Mathematics with Applications, Volume 61, Issue 2, pp. 250-254 (2010). (Elsevier) (Impact Factor: 1.192).

18.  Praveen Kumar Gupta (Subir Das, Kumar Vishal and Ahmet Yildirim), An approximate analytical solution of time-fractional telegraph equation, Applied Mathematics and Computation, Volume 217, Issue 18, pp. 7405-7411 (2011). (Elsevier) (Impact Factor: 1.124).

19.  Praveen Kumar Gupta, Approximate analytical solutions of fractional Benney-Lin equation by reduced differential transformation and homotopy perturbation method, Computer and Mathematics with Applications, Volume 61, Issue 9, pp. 2829-2842 (2011). (Elsevier) (Impact Factor: 1.192).

20.  Praveen Kumar Gupta (with Ahmet Yildirim and Kabindra Nath Rai), Application of He’s homotopy perturbation method for multi-dimensional fractional Helmholtz equation, International Journal of Numerical Methods for Heat and Fluid Flow, In Press (2011) (Emerald) (Impact Factor: 0.790).

21.  Praveen Kumar Gupta (with Dharmendra Tripathi and Subir Das), Influence of Slip Condition on Peristaltic Transport of a Viscoelastic Fluid with Fractional Burgers’ model, Thermal Sciences, doi: 10.2298/TSCI090924043T, In Press (2011) (Vinča Institute of Nuclear Sciences) (Impact Factor: 0.620).

22.  Praveen Kumar Gupta (with Subir Das), Application of Homotopy Perturbation Method and Homotopy Analysis Method to Fractional Vibration Equation, International Journal of Computer Mathematics, Volume 88, Issue 2, pp. 430-441 (2011) (Taylor & Francis) (Impact Factor: 0.478).

23.  Praveen Kumar Gupta (with Subir Das), Homotopy Analysis Method for Solving Fractional Hyperbolic Partial Differential Equations, International Journal of Computer Mathematics, Volume 88, Issue 3, pp. 578 – 588 (2011), (Taylor & Francis) (Impact Factor: 0.478).

24.  Praveen Kumar Gupta (with Subir Das and Suryasarathi Barat), A Note on Fractional Schrodinger Equation, Nonlinear Science Letters A, Volume 1, Issue 1, pp. 91-94 (2010) (Asian Academic Publisher Limited).

25.  Praveen Kumar Gupta (with Subir Das, Rajnesh Kumar and Hossein Jafari), Approximate analytical solutions for Fractional space- and time- partial differential equations using homotopy analysis method, Applications & Applied Mathematics, Volume 5, Issue 10, 1641-1659 (December 2010) (Prairie View A&M University, USA).

26.  Praveen Kumar Gupta (Shantanu Saha Ray, Subir Das and Kumar Vishal), Homotopy Analysis Method for solving Fractional Diffusion equation, International Journal of Applied Mathematics and Mechanics, Accepted (2011).

27.  Praveen Kumar Gupta (Subir Das and Kumar Vishal), Approximate analytical solution of diffusion equation with fractional time derivative using optimal homotopy analysis method, Surveys in Mathematics and its Applications, Accepted (2011).



Contact:

Present Address:
Department of Applied Mathematics,
Institute of Technology,
Banaras Hindu University,
Varanasi - 221 005,
India.

Phone No. +91-9453555044
e-mail : praveen.rs.apm@itbhu.ac.in

 
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