Abstract In this paper we prove the fractional Gagliardo-Nirenberg inequality on homogeneous Lie groups. Also, establish weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type for Riesz potential The obtained Lyapunov is new already in classical setting of $\mathbb {R}^{N}$ ℝ N</mm...

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for stability proposed networks using theory discrete fractional calculus, Laplace transform, and Mittag–Leffler functions. In order to guarantee global asymptotic stability, adequate criteria are determined Lyapunov’...

In this paper, a novel three-dimensional autonomous chaotic system is proposed. The proposed system contains four variational parameters, a cubic nonlinearity term (i.e. product of all the three states) and exhibits a chaotic attractor in numerical simulations. The basic dynamic properties of the system are analyzed by means of equilibrium points, Eigen values and Lyapunov exponents. Finally, t...