A new self-organization of complex networks structure generalized by a new class of fractional differential equations generated by 3D-gamma function

Abstract

In this note, we suggest a generalization of gamma function to be 3D-gamma function. As a consequence, some special functions are generalized including the Mittag–Leffler function. Moreover, we utilize the generalized Mittag–Leffler to extend the AB-fractional calculus. Examples are introduced to cover our theory. The solvability of abstract Riccati equation is considered, and Hyers–Ulam stability is discovered in the sequel. Based on the new study, we design new stable of Self-organization in complex networks (SOCNs).