ABSTRACT
Motivated mainly by certain interesting recent new extensions of the incomplete generalized hypergeometric function by means of the incomplete Pochhammer symbols (λ; κ)ν and [λ; κ]ν, we introduce here the family of the incomplete generalized Mittag-Leffler functions. We then systematically investigate several properties of these incomplete generalized Mittag-Leffler functions including, for example, certain basic properties and various integral transforms representations. Certain properties of the Riemann-Liouville fractional integrals and derivatives associated with the incomplete generalized Mittag-Leffler functions are investigated. Some interesting special cases of our main results are also pointed out. Finally, as an application, we established the solution to the kinetic equations.
