Fractional distributional representation of gamma function and the generalized kinetic equation

Abstract

Motivated by the recent research about non-integer order derivatives of Dirac delta function, we use a fractional Taylor series to explore a fractional distributional representation of gamma function. It proved significant to develop a novel fractional kinetic equation, which is an essential mathematical model to measure the degree of transformation in the chemical structure of stars (sun) as a key component of our environment. In addition to the classical solution of the formulated fractional kinetic equation, the distributional solution is also attained which is not possible without using fractional derivatives of Dirac delta function. Novel identities involving the gamma function are obtained using several fractional transforms. Convergence of new series is proved using the theory of distributions leading to further new applications.

Keywords

• Fractional derivatives of delta function
• Taylor series-function
• Kinetic equation