This article considers a fractional-order neuron model under an electromagnetic field in terms of generalized Caputo fractional derivatives. The motivation for incorporating fractional derivatives in the previously proposed integer-order neuron model is that the fractional-order model impresses with efficient effects of the memory, and parameters with fractional orders can increase the model performance by amplifying a degree of freedom. The results on the uniqueness of the solution for the proposed neuron model are established using well-known theorems. The given model is numerically solved by using a generalized version of the Euler method with stability and error analysis. Several graphical simulations are performed to capture the variations in the membrane potential considering no electromagnetic field effects, various frequency brands of external forcing current, and the amplitude and frequency of the external magnetic radiation. The impacts of fractional-order cases are clearly justified.

We provide sufficient conditions for the existence, uniqueness and global Mittag–Leffler stability for the solutions of fractional difference model of bidirectional associative memory (BAM) neural networks. Before proceeding to the main results, we introduce the newly established discrete fractional calculus and expose some of its features. The techniques of Lyapunov function and Lyapunov direct method are then employed to prove the main results. We give two examples to verify and illustrate the theory.