The generalized p-k-Mittag-Leffler function and solution of fractional kinetic equations

Katugampola kinetic fractional equation with its solution

“…Over the last decades, kinetic fractional equations in many forms have been widely used in describing and solving a variety of important astrophysics and physics (see, e.g. [1,3,9,10,11,12,13,14,15,17,18,24,25,26]) problems. The special functions with their applications (such as Bessel's function, Hypergeometric function, Legender function, and many others) used in the solutions of fractional differential equations.…”

Estimation of certain integrals with extended multi-index Bessel function

“…The Bessel function has gained importance and popularity due to its applications in the problem of wave propagation, cylindrical coordinate system, heat conduction in cylindrical object and static potential etc. In the recent years, some generalizations (unification) and number of integral transforms of Bessel functions have been given by many mathematicians and physicist as well as engineers for example: Choi et al [3], Kiryakova [7], Kamarujjama and Khan [8], Khan et al [9], Kamarujjama et al [10], Khan et al [12] and Khan and Ghayasuddin [13]. Recently, Choi and Agarwal [4] introduced and studied various properties of generalized multiindex Bessel function and then discussed an interesting unified integrals formulas involving the generalized multiindex Bessel function.…”