Prof.  Manoj  Sharma
RJIT, BSF, ACADEMY, TEKANPUR,  India

Title: The Fractional Kinetic Equations

Abstract:

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, F(x) ∼|x|−α, α>0 where F(x) is the distribution function. In such cases, moments E(|x|p) exist only if p<α and integer order moments greater then α diverge. This type of problem arises in the distributions where power law statistics appear in many fields of applied science.

Biography: