Abstract
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.
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Chaurasia, V.B.L., Pandey, S.C. On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions. Astrophys Space Sci 317, 213–219 (2008). https://doi.org/10.1007/s10509-008-9880-x
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DOI: https://doi.org/10.1007/s10509-008-9880-x
Keywords
- Generalized function for the fractional calculus and fractional kinetic equations: general
- Fractional kinetic equations and generalized functions: individual (the G-function and its relationships with other special functions, the Mellin-Barnes contour integral representation of the G-function, generalized fractional kinetic equations)