The primarily object of this article is to derive the solutions of modified fractional kinetic equations (MFKEs) containing the incomplete Aleph functions by using the application of Elzaki and inverse Elzaki transforms and hereto we also established some novel results such as the Elzaki transform of well-known the Riemann–Liouville operator and the incomplete Aleph functions (IAFs). The solutions of modified FKEs discusses in this article can be utilized to figures out the variation of the chemical composition in our solar system. In this article, we also see that the character of thermonuclear function is presented in terms of the incomplete?-functions and many more special functions through some interesting corollaries. Finally, we established here a compact and easily figure out solutions in form of incomplete special functions and display the graphs of the obtained results in the end of this article to show the behavior of integral operator of fractional order on reaction rate of the particle. Furthermore, results holds here are also associated to the recent investigation of feasible astrophysical solutions of solar system problems. The derived results notify the known results more precisely.
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