Extension of the truncated M-fractional derivative linked to multivariate generalized Mittag-Leffler function demonstrating classical characteristics

The primary objective of this paper is to introduce a novel concept called the truncated M-fractional derivative in conjunction with the multivariate generalized Mittag-Leffler function. This derivative is denoted by DMα,ξj,ηj,lj,μj,νji(⋅), where the parameter α, representing the derivative order, adheres to the condition 0<α<1. The symbol M is utilized to indicate that the function subjected to differentiation involves the truncated multivariate Mittag-Leffler function E(ηj;1;νj)(ξj;lj;μj)i(⋅). Notably, the operator DMα,ξj,ηj,lj,μj,νji(⋅) maintains the fundamental properties of integer-order calculus. Additionally, the paper presents the corresponding fractional integral, naturally leading to a result which could be seen as an inverse property. The conclusion of the paper showcases various special cases that emerge by altering parameter values, encompassing both well-known scenarios and novel instances.