FRACTIONALCALCULUSOPERATORSOFTHEGENERALIZED EXTENDEDMITTAG-LEFFLERFUNCTIONANDRELATED JACOBITRANSFORMS

Abstract

Ouraimistoobtaincertainimageformulasofthep–extendedMittagLeffler functionEγ α,β,p(z)byusingSaigo’shypergeometric fractional integral and differentialoperators.CorrespondingassertionsfortheclassicalRiemann-Liouville (R-L)andErd´elyi-Kober (E-K) fractional integral anddifferential operatorsare established. All theresultsarerepresentedintermsof theHadamardproductof thep–extendedMittag-Leffler functionEγ λ,µ,p(z)andFox-Wright functionrΨs(z). WealsoestablishedJacobi and itsparticularassertions for theGegenbauerand Legendretransformsofthep–extendedMittag-LefflerfunctionEγ α,β,p(z).