A Novel Fractional-Order Neutral-Type Two-Delayed Neural Network: Stability, Bifurcation, and Numerical Solution

Abstract

In this paper, we propose a novel fractional-order neutral-type delay neural network (FNDNN) considering two delay variables in terms of the Caputo fractional derivatives. We prove the existence of a unique solution within the given time domain. We analyse the bifurcation with respect to both delay parameters and the initial state's stability of the FNDNN. We derive the numerical solution of the proposed FNDNN using a recently proposed algorithm. We provide the necessary graphical simulations to justify the correctness of our theoretical proofs. We investigate how both delay parameters affect stability and induce bifurcations in the FNDNN. Also, we check the influence of fractional orders on the dynamical behaviour of the FNDNN. We find that, in comparison with the integer-order case, the proposed FNDNN has faster convergence performance.