On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions

In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving the G -function, a generalized function for the fractional calculus. This new generalization can be used for the computation of the change of chemical composition in stars like the Sun. The Mellin-Barnes contour integral representation of the G -function is also established. The manifold generality of the G -function is discussed in terms of the solution of the above fractional kinetic equation. A compact and easily computable solution is established. Special cases, involving the generalized Mittag-leffler function and the R -function, are considered. The obtained results imply more precisely the known results.