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

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 MellinBarnes 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.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)

Fractional integrals and solution of fractional kinetic equations involvingk-Mittag-Leffler function

“…Especially, the kinetic equations describe the continuity of motion of substance. The extension and generalization of fractional kinetic equations involving many fractional operators were found in [14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Solutions of Generalized Fractional Kinetic Equations via Sumudu Transforms Involving Bessel-Struve Kernel Function

“…The details about fractional kinetic equations and solutions, one can refer to [11,[17][18][19][20][21][22][23][24][25]30] 3. Solution of generalized fractional Kinetic equations involving (1.…”

Certain fractional kinetic equations involving the product of generalized k-Bessel function

“…In recent years, unified integrals involving Special functions attract the attention of the many researchers due to various application point of view(see, [24,7]). In the sequel, Diaz and Pariguan [8] introduced the k-Pochhemmer symbol and k-gamma function defined as follows: They gave the relation with the classical Euler's gamma function(see [2,23]) as:…”

“…Especially, the kinetic equations describe the continuity of motion of substance. The extension and generalization of fractional kinetic equations involving many fractional operators were found [26,20,13,21,22,23,24,7,9,5,6,12,14,2].…”