In view of the usefulness and a great importance of the kinetic equation incertain astrophysical problems, the authors develop a new and further generalized form ofthe fractional kinetic equation in terms of Aleph-function by using Sumudu transform. Thisnew generalization can be used for the computation of the change of chemical compositionin stars like the sun. The manifold generality of the Aleph-function is discussed in termsof the solution of the above fractional kinetic equation. The main results, being of generalnature, are shown to be some unication and extension of many known results given, forexample, by Saxena et al. [23, 25, 31], Saxena and Kalla [22], Chaurasia and Kumar [6],Dutta et al. [8], and etc.