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Computable Extension of New Advanced Fractional Kinetic Equation

Manoj Sharma, Laxmi Morya, Rajshree Mishra

Abstract


Abstract

First, we obtain computable extensions of advanced fractional kinetic equation. The aim of this survey 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, provide 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. In late years, fractional kinetic equations are considered because of their helpfulness and significance in mathematical physics, particularly in astrophysical issues. In astrophysics, kinetic equations assign an arrangement of differential equations, portraying the rate of progress of chemical composition of a star for every species as far as the response rates for pulverization and creation of that species are concerned. Techniques for demonstrating procedures of pulverization and generation of stars have been created for bio-chemical reactions and their insecure harmony states and for concoction response systems with unstable states, oscillations and hysteresis. The point of present paper is to discover the arrangement of summed up fragmentary request motor condition, utilizing another exceptional capacity. The outcome got here is decently widespread in nature. Exceptional cases, identifying with the Mittag-Leffler work are additionally considered. 

Mathematics Subject Classification: 33C60, 33E12, 82C31, 26A33

Keywords: Fractional kinetic equation, Generalized function, Riemann-Liouville operator, Laplace transform, modified Riemann-Liouville fractional derivative operator, differential equation

Cite this Article

Manoj Sharma, Laxmi Morya, Rajshree Mishra. Computable Extension of New Advanced Fractional Kinetic Equation. Research & Reviews: Discrete Mathematical Structures. 2017; 4(2): 26–32p.



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