Abstract: This paper is devoted to estimating the bound of the Lyapunov exponents for the Caputo–Hadamard fractional differential system. First, using the Gronwall inequality, we analyze the continuous dependence of the solution to ...

Abstract: Dimension reduction of dynamical system is a significant issue for technical applications, as regards both finite dimensional system and infinite dimensional systems emerging from either science or engineering. Center ...

Abstract: Lyapunov–Schmidt reduction is one of the powerful and significant methods to simplify nonlinear ordinary differential systems (ODSs) with standard formulation. In this paper, we extend Lyapunov–Schmidt reduction to ...

Abstract: This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamard-type fractional derivative of a given function can ...

Abstract: In this study, we describe the fractional convection operator for the first time and present its discrete form with second-order convergence. A numerical scheme for the fractional-convection–diffusion equation is also ...

Abstract: This article focuses on investigating fractional Lyapunov exponents for generalized ψ-fractional differential systems. By employing a new and more suitable definition, we derive an expression for the fractional Lyapunov ...