Generalized Fractional Integral Formulas for the k-Bessel Function

Abstract

The aim of this paper is to deal with two integral transforms involving the Appell function as their kernels. We prove some compositions formulas for generalized fractional integrals with k-Bessel function. The results are expressed in terms of generalized Wright type hypergeometric function and generalized hypergeometric series. Also, the authors presented some related assertion for Saigo, Riemann-Liouville type, and Erdélyi-Kober type fractional integral transforms.

A Study on Generalized Multivariable Mittag-Leffler Function via Generalized Fractional Calculus Operators

“…Recently, Gurjar et al [1] introduced a multivariable generalized Mittag-Leffler (M-L) function; this function and its special cases have recently found various essential applications in solving problems in physics, biology, engineering and applied sciences (see; [2][3][4][5]). The function is defined for , , , ∈ C and min 1≤ ≤ {R( ), R( ); R( ), R( )} > 0, , > 0; < + R( ); = 1, 2, .…”

Class of integrals and applications of fractional kinetic equation with the generalized multi-index Bessel function

“…Now a days, the recent research outputs are indicating that, the dimension of fractional order calculus (FOC) is tuned into the practical applications on science and engineering. Also, it is found that, the fractional calculus describes in models and respective other physical phenomena (see [6,16,18,19,22,23,24,25,26,37,38,39,45,47,48,49,50]).…”