On the solutions of certain fractional kinetic equations involving k-Mittag-Leffler function

Abstract

We develop a new generalized form of the fractional kinetic equation involving a generalized k-Bessel function. The generalized k-Mittag-leffler function E γ,q k,α,β (.) is discussed in terms of the solution of the fractional kinetic equation in the present paper. The results obtained here are quite general in nature and capable of yielding known and as well new results.

From continuous-time random walks to controlled-diffusion reaction

“…The methods and the techniques applied in this work allow a new approach to the problems associated with precipitation of particles on a surface with irregularities in which irregularities act as reaction-traps. In addition, this work opens possibilities to investigate the coupled controlled-diffusion reaction in the context of fractional derivatives or memory function associated with special functions [70,71].…”

A New Representation of the k-Gamma Functions

“…It is remarkable that k-gamma functions and related k-Pochhammer symbols are more the functions of the fractional calculus. For example, Agarwal et al [6] have solved fractional kinetic equations comprising of k-Mittag-Leffler functions. Set et al have used the analogue to the Riemann-Liouville singular kernel at k-calculus in [7].…”

“…Set et al have used the analogue to the Riemann-Liouville singular kernel at k-calculus in [7]. For more comprehensive and detailed studies of related works, I refer the interested reader to [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and associated references therein. The literature review for k-gamma functions motivates us to state "on the one hand k-gamma functions excited to mathematician for the analysis of mathematical concepts in a new way and on the other applications of these functions in diverse problems are fundamental".…”

Application of Laplace Transform on Fractional Kinetic Equation Pertaining to the Generalized Galué Type Struve Function

“…Particularly, the kinetic equations define the continuity of motion of substance and are the elementary equations of mathematical physics and natural science. The extension and generality of fractional kinetic equations and various fractional operators with special functions were found (Agarwal et al [1], Amsalu and Suthar [2], Baleanu et al [3,4], Chaurasia and Pandey [5], Choi and Agarwal [6,7], Zaslavsky [8], Gupta and Parihar [9], Gupta and Sharma [10], Haubold and Mathai [11], Kumar et al [12], Nisar et al [13], Saxena et al [14][15][16], Saichev and Zaslavsky [17], Suthar et al [18], and Tariboon et al [19]). In view of the effectiveness and a great significance of the kinetic equation in some astrophysical problems the authors develop a further generalized form of the fractional kinetic equation involving generalized Galué type Struve function.…”