Solutions of generalized fractional kinetic equations involving Aleph functions

In view of the usefulness and great importance of the kinetic equation in certain astrophysical problems, the authors develop a new and further generalized form of the fractional kinetic equation in terms of the Aleph-function by using the Sumudu transform. This new generalization can be used for the computation of the change of chemical composition in stars like the sun. The manifold generality of the Aleph-function is discussed in terms of the solution of the above fractional kinetic equation. The main results, being of general nature, are shown to be some unification and extension of many known results given, for example, by Saxena et al. [23, 25, 31], Saxena and Kalla [22], Chaurasia and Kumar [6], Dutta et al. [8], etc. AMS subject classifications: 26A33, 44A10, 44A20, 44A35, 33C20, 33C45, 33C60, 33E12