In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle.

This paper treats a new approach to the problem of periodic signal estimation. The idea is to model the periodic signal as a function of the state of a second order nonlinear ordinary differential equation (ODE). This is motivated by Poincare theory which is useful for proving the existence of periodic orbits for second order ODEs. The functions of the right hand side of the nonlinear ODE are t...

Power electronic is rich in nonlinear dynamic. Its operation is characterized by cyclic switching of circuit topologies, which gives rise to different nonlinear behaviors. Among power electronic converters, DC/DC buck converters have been studied with constant-frequency pulse-width modulation feedback control in continuous conduction mode. Time-domain and phase-space plots for several periodic ...

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative te...

We study the question of nonexistence of small spatially periodic, timeperiodic solutions for cubic nonlinear Schrödinger equations. We prove that for almost any value in a bounded set of possible temporal periods, there is an amplitude threshold, below which any initial value is not the initial value for a time-periodic solution. The proof requires a certain level of Sobolev regularity on solu...

We are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws. The main objective of this paper is to present an analytical approach and to explore its applications to studying the large-time behavior of periodic entropy solutions of hyperbolic conservation laws. The asymptotic decay of periodic solutions of nonlinear hyperbolic conservation laws is an import...

The basic principles of an eficient new methodology for the calculation of the non-sinusoidal periodic steady state in system with nonlinear and timevarying components are described. All linear parts, including the network and part of he loads. are represented in the frequency domain, while nonlinear and time-varying components, mainly loads, are represented in the time domain. This hybrid proc...

In this paper, He's amplitude-frequency formulation is used to obtain a periodic solution of a nonlinear oscillator. We illustrate that He's amplitude-frequency formulation is very effective and convenient and does not require linearization or small perturbation. The obtained results are valid for the whole solution domain with high accuracy.

Rogue periodic waves stand for rogue waves on the periodic background. Two families of traveling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and twofold Darboux transformations, we construct explicitly the rogue periodic waves of the mKdV equation. Since the dn-periodic wave i...

In this paper, we consider the Schrodinger-KdV system with time-dependent boundary external forces. We give conditions on forces sufficient for unique existence of small solutions bounded all time. Then, investigate solution, periodic quasi-periodic solution and almost system. The main difficulty is nonlinear terms in equations, order to overcome difficulty, establish some properties semigroup ...