The extended Mittag-Leffler function via fractional calculus

Generalized Mittag-Leffler Type Function: Fractional Integrations and Application to Fractional Kinetic Equations

“…The integral operators of the types (8) and (9) have been introduced by Marichev [31] and later extended and studied by Saigo and Maeda [32]. Recently, many researchers (see [33][34][35]) have studied the image formulas for MSM FIOs involving various special functions.…”

“…Many more generalizations and extensions of MLF widely studied recently [9,10]. Also, the MLF performs an important role in physics and engineering problems.…”

Fractional Integrations of a Generalized Mittag-Leffler Type Function and Its Application

“…Fractional calculus of special functions is studied by many authors in a different point of view due to its importance in various applied science topics. Many extensions and generalizations are established for special functions in view of fractional calculus [24][25][26][27][28][29][30][31][32][33]. It should be noted that the idea of fractional treatment has also been studied in discrete mathematics [34].…”

Hadamard And Fejer-Hadamard Type Inequalities for Convex and Relative Convex Functions via an Extended Generalized Mittag-Leffler Function

“…(i) By setting p = 0, it reduces to the Salim-Faraj function E γ,δ,k,c µ,α,l (t) defined in [12]. (ii) By setting l = δ = 1, it reduces to the function E γ,k,c µ,α (t; p) defined by Rahman et al in [11]. (iii) By setting p = 0 and l = δ = 1, it reduces to the Shukla-Prajapati function E γ,k µ,α (t) defined in [13] (see also [14]).…”

“…(ii) By setting l = δ = 1, they reduce to the fractional integral operators defined by Rahman et al in [11].…”