The bifurcations in a fractional-order neutral bidirectional associative memory neural network(FONBAMNN) in the inclusion of different neutral delays are deliberated. By the aid of the presented assumptions, the devised FONBAMNN involving four nonidentical delays is subtly transformed into the one with unique delay. Then the outcomes with regard to delay-dependent bifurcations are cultivated by means of the analytic methodology of the characteristic equation. It is evidenced experimentally that the stability performance of the developed FONBAMNN can be neatly maintained when extracting a lesser time delay, and the bifurcation fruits are finely authenticated by employing the bifurcation graphs. Additionally, it proclaims that fractional orders are instrumental in ameliorating the stability of FONBAMNN in comparison with the conventional integer-order counterpart. The efficiency of the developed theory is lastly underpinned by numerical experimentations.