In this paper, an analytical scheme [the generalized Sinh–Gordon equation method) with a
new fractional operator (ABR fractional operator] is employed to find novel computational …

This research paper elucidates solitary, compacton, and peakon computational solutions,
and numerical solutions of the nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) …

Motivated by the importance of discrete structures of neuron networks, a neural field lattice
system arising from the discretization of neural field models in the form of integro-differential …

In this paper, we study the asymptotic behavior of non-autonomous fractional stochastic
lattice systems with multiplicative noise. The considered systems are driven by the fractional …

Two Hopfield-type neural lattice models are considered, one with local n-neighborhood
nonlinear interconnections among neurons and the other with global nonlinear …

We discuss multichromatic front solutions to the bistable Nagumo lattice differential
equation. Such fronts connect the stable spatially homogeneous equilibria with spatially …

We survey some recent results on traveling waves and pattern formation in spatially discrete
bistable reaction-diffusion equations. We start by recalling several classic results concerning …

We show existence and uniqueness of traveling front solutions to a class of neural field
equations set on a lattice with infinite range interactions in the regime where the kinetics of …

In this work we study travelling wave solutions to bistable reaction–diffusion equations on bi-
infinite k-ary trees in the continuum regime where the diffusion parameter is large. Adapting …

We consider a nonlocal discrete nonlinear Schrödinger equation with delays. We prove that
the process associated with the non-autonomous model possesses a pullback attractor. As a …