A further extension of Mittag-Leffler function

By M. Andrić, G. Farid, Josip E. Pecaric. Fractional Calculus and Applied Analysis, 2018

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Abstract In this paper an extended generalized Mittag-Leffler function Eρ,σ,τδ,r,q,c(z;p) $\begin{array}{} \displaystyle E_{\rho,\sigma,\tau}^{\delta,r,q,c}(z;p) \end{array}$ and the corresponding fractional integral operator εa+,ρ,σ,τw,δ,q,r,cf $\begin{array}{} \displaystyle \varepsilon_{a^{+},\rho,\sigma,\tau}^{w,\delta,q,r,c}f \end{array}$ are defined and used to obtain generalizations of Opial-type inequalities due to Mitrinović and Pečarić. Also, some interesting properties of this function and its integral operator are discussed. Several known results are deduced.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/335da0980cb60dcbe22e0ed9c6e3b317bca976f9