The ( k , s ) $(k,s)$ -fractional calculus of k-Mittag-Leffler function

Abstract

In this paper, we introduce the (k, s)-fractional integral and differential operators involving k-Mittag-Leffler function E δ k,ρ,β (z) as its kernel. Also, we establish various properties of these operators. Further, we consider a number of certain consequences of the main results.

On Extended General Mittag–Leffler Functions and Certain Inequalities

“…For the applications of and related results containing Mittag-Leffler functions, see [10,11]. For details on Hermite-Hadamard-type inequalities involving fractional integrals via different classes of convex functions, see Kunt et al [12], Mihai [13,14], Mihai and Mitroi [15], Nisan et al [16], Noor et al [17], Sarikaya and Yildirim [18], and others.…”

Fractional Hermite-Hadamard inequalities containing generalized Mittag-Leffler function

“…Işcan et al [ 6 ] established new fractional estimates of Hermite-Hadamard-type inequalities via harmonic convex functions. For more details on Hermite-Hadamard inequalities involving fractional integrals; see Mihai [ 13 , 14 ], Mihai et al [ 15 ], Awan et al [ 16 ], Kunt et al [ 7 ], Sarikaya et al [ 17 ], Nisan et al [ 18 ], and references therein. Latif et al [ 8 ] gave the following definition.…”

On Grüss inequalities within generalized K-fractional integrals

“…There are numerous problems wherein fractional derivatives (non-integer order derivatives and integrals) attain a valuable position [1][2][3][4][5][6][7][8][9]. It must be emphasized that fractional derivatives are furnished in many techniques, especially, characterizing three distinct approaches, which we are able to mention in an effort to grow the work in certainly one of them.…”

“…These are called generalized K-fractional integrals. For such operators, we refer to [4,[18][19][20] and the works cited in them.…”