A further extension of Mittag-Leffler function

In this paper an extended generalized Mittag-Leffler function Eδ,r,q,c ρ,σ, (z; p) and the corresponding fractional integral operator ηw,δ,q,r,c a+,ρ,σ, are defined and used to obtain generalizations of Opial-type inequalities due to Mitrinović and Peĉarić. Also, some interesting properties of this function and its integral operator are discussed. Several known results are deduced. © 2018 Diogenes Co., Sofia 2018.