<p>The paper is devoted to present considerations concerning the solvability on a bounded interval of a system of nonlinear integral equations, which create the generalization of a fractional-order neuron model under the electromagnetic field expressed in terms of Caputo fractional derivatives. Our approach depends on replacing the neuron models in question by a system of nonlinear integral equations of the Volterra–Stieltjes type. That enables us to apply suitable tools of nonlinear analysis and to obtain a transparent and easy-to-apply result. The established criteria significantly extend and refine the solvability theory for this class of generalized fractional neuron models.</p>