Novel extended mixed controller design for bifurcation control of fractional-order Myc/E2F/miR-17-92 network model concerning delay

MiR-17-92 has a vital effect on the adjustment of the Myc/E2F protein in chemistry. In this work, we propose a novel fractional-order delayed Myc/E2F/miR-17-92 network model that revels the relation between miR-17-92, E2F, and Myc. Taking advantage of Laplace transform, we obtain the characteristic equation of the established fractional-order delayed Myc/E2F/miR-17-92 network model. By virtue of stability theorem and bifurcation criterion of fractional-order dynamical equation, a novel delay-independent condition guaranteeing the stability and the generation of bifurcation phenomenon of the involved model is acquired. By exploiting a proper extended mixed controller (including PD epsilon P{D}<^>{\epsilon } $$ controller and delayed feedback controller), we efficiently control the stability domain and the emergence of bifurcation for the the involved model. By utilizing another suitable extended mixed controller (including PD & thetasym;$$ P{D}<^>{\vartheta } $$ controller and hybrid controller), we can successfully adjust the stability domain and the emergence of bifurcation for the the involved model. The research indicates that delay plays a vital role in stabilizing system and controlling bifurcation of the fractional-order delayed Myc/E2F/miR-17-92 network model. Computer experiment results illustrate the scientificity of the gained key analytical outcomes. The acquired results in this research are totally innovative and own immense theoretical meaning in regulating the concentrations of different proteins.