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

Abstract

We develop a new and further generalized form of the fractional kinetic equation involving generalized k-Bessel function. The manifold generality of the generalized k-Bessel function 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 a very large number of known and (presumably) new results.

A New Representation of the k-Gamma Functions

“…For more such properties of k-gamma and related functions, we refer the reader to [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and related bibliography therein. The subsequent Section 2.2 is taken from author work [22].…”

“…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".…”

“…The results (10)(11)(12)(13)(14)(15) are also straightforward by using the characteristics of delta function for the Fourier transformation. First, we consider proving result 10.…”

Fractional operators with generalized Mittag-Leffler k-function

“…A useful generalization of the Mittag-Leffler function, the so-called Mittag-Leffler k-function has been introduced and studied in [6]. Many mathematicians discussed and obtained new results [7][8][9][10][11][12][13], seen as theoretical developments to the fractional operators. These considerations have led various researchers in the field of special functions for exploring possible extensions of and applications to the Mittag-Leffler function.…”

On new applications of fractional calculus

“…In recent years there has appeared a great deal of literature discussing the application of the aforementioned fractional calculus operators in a number of areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, summation of series, et cetera) and now stands on fairly firm footing through the research contribution of various authors (cf., e.g., [1,2,3,4,5,6,7,8,9,10,11,12,14,16,17] ). Here, we aim derive some summations series concerning generalized hypergeometric function which are applications of the one of Samko result.…”