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

Abstract

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

Keywords

• fractional integral
• k-fractional integral operator
• ( k , s ) $(k,s)$ -fractional integral
• ( k , s ) $(k,s)$ -fractional differential
• k-Mittag-Leffler function