A generalization of q-Mittag-Leffler Function with Four Parameters
Riemann Liouville fractional q-integral and derivative operator
Weyl-type fractional q-integral and derivative operator
Kober-type fractional q-integral and derivative operator
basic-analogue of Mittag-Leffler function
q-Laplace transform
q-Mellin transform
The main purpose of this article is to introduce two different new basic analogue of the four parameters Mittag-Leffler function. Some q-integral representations and q-Mellin transforms for these q-analogues are derived. We have also obtained Riemann Liouville-type, Weyl-type and Kober-type fractional q-integrals and q-derivatives for these q-analogues of the four parameter Mittag-Leffler functions as the applications in q-fractional calculus.