A novel computable extension of fractional kinetic equations arising in astrophysics. (English) Zbl 1359.34006

Chaurasia, V. B. L.; Singh, Yudhveer

Int. J. Adv. Appl. Math. Mech. 3, No. 1, 1-9 (2015).

Summary: The objective of the present paper is to develop the solutions of generalized fractional kinetic equations involving the generalized Mittag-Leffler function and I-function. The use of mathematical physics in distinguished astrophysical problems has attracted astronomers and physicists to special attention on available mathematical tools that can be used in solving several problems of astrophysics. The manifold generality of the generalized Mittag-Leffler and I-function is discussed in terms of the solution of the above fractional kinetic equations. Special cases involving the generalized Mittag-Leffler function, \(\bar{H}\)-function, Fox H-function and generalized M-series are considered. The obtained results imply the known results more precisely.

MSC:

34A08	Fractional ordinary differential equations
33E12	Mittag-Leffler functions and generalizations
33C60	Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
85A04	General questions in astronomy and astrophysics

Keywords:

fractional kinetic equation; generalized Mittag-Leffler function; I-function; Riemann-Liouville operator; generalized M-series; Laplace transform