ON EXTENDED k-GENERALIZED MITTAG-LEFFLER FUNCTION AND ITS PROPERTIES

In this current paper, we are using the concept of extension of the beta function to define an extended k-generalized Mittag-Leffler function (GMLf) (Formula presented). There are four sections included in this paper containing some properties of the above-described function, like derivatives, integral representation, and integral transform. The establishment of some recurrence relations has also been done. We also derive the extended k-GMLf from the extended k-Riemann-Liouville (R-L) fractional derivative of generalized MLf. Numerous former results studied by many researchers can also be derived as special cases of our results. © (2025), (American Institute of Mathematical Sciences). All rights reserved.