Keynote speaker

Computable extensions of advance fractional kinetic equation and class of levy-type probabilities

Dr Manoj Sharma, PhD

Dr Manoj Sharma, PhD

Department of Applied Mathematics
Rustamji Institute of Technology. Tenkapur. India

Abstract

The talk divided into two sections: First we obtain computable extensions of advanced fractional kinetic equation and then in second section applied Modified RiemannLiouville fractional Integral ie ms-operator and differential equation for a Class of Levy-type probabilities. The aim of this talk is to explore the behavior of physical and biological systems from the point of view of fractional calculus. Fractional calculus, integration and differentiation of an arbitrary or fractional order, provides new tools that expand the descriptive power of calculus beyond the familiar integer-order concepts of rates of change and area under a curve. Fractional calculus adds new functional relationships and new functions to the familiar family of exponentials and sinusoids that arise in the area of ordinary linear differential equations. Among such functions that play an important role, we have the Euler Gamma function, the Euler Beta function, the Mittag-Leffler functions, the Wright and Fox functions, M-Function, K-Function and so forth.The Fractional Calculus applied in The distributions of a extensive variety of physical, biological, and man-made phenomena approximately follow a power law over a wide range of magnitudes. More than a hundred power-law distributions have been identified in biology (e.g. species extinction and body mass), in physics (e.g. sand pile avalanches and earthquakes), and the social sciences (e.g. city sizes and income).When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law. A power law distribution is a special kind of probability distribution. Fractional moments are very useful in dealing with random variable with power law distributions.

In recent year’s fractional kinetic equation are studied due to their usefulness and importance in mathematical physics, especially in astrophysical problems. In Astrophysics kinetic equations designate a system of differential equations, describing the rate of change of chemical composition of a star for each species in terms of the reaction rates for destruction and production of that species. Methods for modeling processes of destruction and production of stars have been developed for bio-chemical reactions and their unstable equilibrium states and for chemical reaction networks with unstable states, oscillations and hysteresis.The aim of present paper is to find the solution of generalized fractional order kinetic equation, using a new special function. The results obtained here is moderately universal in nature. Special cases, relating to the Mittag-Leffler function is also considered.

Information about speaker

Head of Department of Applied Mathematics
Former Head of Department of Computer Applications
Rustamji Institute of Technology.
BSF, Academy, Tenkapur, Gwalior, MP, India, 474001
Executive member of Gwalior Academy of Mathematical Sciences

RECOGNITION / AWARDS & PRIZES WON:

  • Selected among the five best research papers for the Young Scientist Award in the International Conference FDA08 held in Chankaya University , Ankara Turkey 05-07 Nov. 2008.
  • Selected Department of Science and Technology Fellowship after securing 85% marks in SERC, School at CMS Kerla, (INDIA), held in 14 March- 15 April 2005.
  • Honored Young Researcher Award for International Research Gwalior Academy of Mathematics & Mathematical Sciences (GAMS),(An International level Professional Body) during 14th Annual National Conference of GAMS at IPS College Gwalior (17-19 July 09).
  • Commendation Certificate from IG/Director BSF Academy in 2006 for successful work in stone Laying Ceremony of RJIT
  • Commendation letter from IG/Director BSF Academy in 2010 for successful organization of National Conference.
  • Appreciation Certificate from ADDL. DG/ Director BSF Academy in 2012 for successful organization International Conference on “Special Functions and Their Applications in Science and Engineering and in Symposium on “Fractional Calculus and Its Applications” ICSFA-2011 in Dec. 08-10,2011
  • Commendation Certificate from ADDL. DG/ Director BSF Academy in 2013 for successful organization of Faculty development Programme on “Effective Teaching & Classroom Communication” in 27-05-13 to 01-06-13.
  • Outstanding Young Person Award given by JCI GWALIOR (Gwalior Ratna Alankaran) in the category of Academic Leadership at 48th Charter Nite Ceremony held on 18th April 2012.
  • Outstanding Young Person Award given by Madhya Pradesh Patrakar Association (Out Standing Pratibha Samman Ceremony held on 14h october 2012 at Dabra Gwalior.

EDITOR (INTERNATIONAL JOURNAL/ NATIONAL JOURNAL):
  • Guest Editor of International American Journal of Applied Mathematics and Statistics.
  • Editor of International Journal Napier Indian Advanced Research journal of Sciences.
  • Editor of International STM Journal.
  • Editor of Journal ISMAMS, India.

INVITED TO BE KEYNOTE SPEAKER OF NATIONAL/INTERNATIONAL CONFERENCES:
  • Delivered an Invited Talk at Annual Conference of VIJANANA PARISHAD of INDIA and National conference of JPIT, Guna on “Recent Trends on Applicable Mathematics and Information Technology” held in Dec,03 -05,2009.
  • Delivered an Invited Talk in International Conference on “Special Functions and Their Applications in Science and Engineering and in Symposium on “Fractional Calculus and Its Applications”ICSFA-2011 in Dec. 08-10,2011. at RJIT, BSF, TEKANPUR.
  • Delivered an Invited Talk in 17th Annual Conference of GAMS and National Symposium of JPUT, Guna on “Computational Mathematics and Information Technology “, held in Dec 07 -09,2012.
  • Delivered an Invited Talk at 16 thAnnual Conference of VIJANANA PARISHAD of INDIA and National conference on “Mathematical and Computational Modeling “at Dr. B.R. Ambedkar University, during 24- 26 May 2013.
  • Delivered an Invited Talk in TEQIP-II Sponsored One Week STTP on “Applications of Fixed Point Theory and Nonlinear Analysis for Engineering and Sciences”, “AFPTNAES 2014” at SVNIT, SURAT, during 30th June 2014-04thJuly 2014.
  • Delivered an Invited Talk in EDP-2014 at EDC Cell of MITS, Gwalior, MP, during 12-Sept.2014.
  • Delivered Two Invited Talk in National Conference on “Recent developments in special functions and their applications” during Nov.04-06, 2014 in T.D.P.G. College, Jaunpur U.P..
  • Delivered an Invited Talk in International Conference on “The works of Sriniwasramanujan& their Applications in Science and Engineering” & International Symposium ON “New Trends in Applications of Mathematics in Science And Engineering Specially in Fractional Calculus, Bioinformatics and Special Functions” ICSFA-2014.

MEMBERSHIP OF PROFESSIONAL SOCIETIES:
  • Gwalior Academy of Mathematical Sciences (GAMS),
  • Indian Academy of Mathematics (IAM),
  • Rajasthan Ganita Parishad,
  • Indian Mathematical Society (IMS),
  • ISMAMS, India

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