FRACTIONAL KINETIC EQUATION A NEW PARADIGM

Abstract

The aim of present paper 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 The first accurate use of a derivative of non-integer order is due to the French mathematician S. F. Lacroix in 1819 who expressed the derivative of non-integer order  in terms of Legendre’s factorial symbol G.