Showing papers in "Communications in Nonlinear Science and Numerical Simulation in 2012"

TL;DR: The proposed KH algorithm, based on the simulation of the herding behavior of krill individuals, is capable of efficiently solving a wide range of benchmark optimization problems and outperforms the exciting algorithms.

TL;DR: In this article, a method for finding exact solutions of nonlinear differential equations is considered and modifications of the method are discussed, showing that the method is one of the most effective approaches for solving nonlinear problems.

TL;DR: In this paper, the authors used variational finite element method (FEM) with a local non-similar transformation to solve the non-linear governing equations with associated boundary conditions.

TL;DR: In this article, a 3D autonomous quadratic system with a single stable node-focus equilibrium is shown to be chaotic in the sense of having a positive largest Lyapunov exponent, a fractional dimension, a continuous broad frequency spectrum, and a period-doubling route to chaos.

TL;DR: In this paper, the existence of a solution for impulsive Cauchy problems with fractional derivative is investigated and sufficient conditions for existence of the solutions are established by applying fixed point methods.

TL;DR: In this article, the solutions of fuzzy fractional differential equations (FFDEs) under Riemann-Liouville H-differentiability by fuzzy Laplace transforms are studied.

TL;DR: A novel chaotic improved imperialist competitive algorithm (CICA) is presented for global optimization and the Logistic and Sinusoidal maps are found as the best choices.

TL;DR: A novel image encryption algorithm based on a three dimensional (3D) chaotic map that can defeat the aforementioned attack among other existing attacks is suggested.

TL;DR: In this article, a new base function and an auxiliary linear operator to form a better homotopy is proposed, and a mathematical proof of the convergence is provided for the convergence.

TL;DR: In this paper, the second kind Chebyshev wavelet operational matrix of fractional integration is derived and used to transform the equation to a system of algebraic equations, and the results obtained are compared with the existing ones in open literature.

TL;DR: A sliding mode control law is designed to control chaos in a class of fractional-order chaotic systems and effectiveness of the proposed control scheme is illustrated through numerical simulations.

TL;DR: In this paper, the stagnation point flow of nanofluid near a permeable stretched surface with convective boundary condition is analyzed in the presence of porous medium and internal heat generation/absorption.

TL;DR: In this article, the numerical solution of classes of fractional convection-diffusion equations with variable coefficients is solved by reducing the problem to the solution of linear algebraic equations by expanding the required approximate solution as the elements of shifted Legendre polynomials in time and the Sinc functions in space with unknown coefficients.

TL;DR: In this article, heat and mass transfer analysis for boundary layer stagnation-point flow over a stretching sheet in a porous medium saturated by a nanofluid with internal heat generation/absorption and suction/blowing is investigated.

TL;DR: The security and performance analysis and reliability analysis of the proposed image encryption scheme based on the quantum logistic map are encouraging and it can be concluded that, the proposed scheme is efficient and secure.

TL;DR: In this paper, a fractional-order sliding mode approach is proposed to stabilize and synchronize a class of fractional order chaotic systems in the presence of model uncertainties and external disturbances.

TL;DR: In this article, the operational matrix of fractional derivative of order α in the Caputo sense using the linear B-spline functions is constructed, which reduces such problems to those of solving a system of algebraic equations.

TL;DR: In this article, the free vibration response of single-walled carbon nanotubes (SWCNTs) is investigated using various nonlocal beam theories, including Euler-Bernoulli beam theory, Timoshenko beam theory and Reddy beam theory.

TL;DR: In this paper, the Riccati equation approach was used to design a full-order observer for one-sided Lipschitz nonlinear systems, and the reduced-order observers were designed for the same purpose.

TL;DR: In this paper, some new concepts in stability of fractional differential equations are offered from different perspectives, such as Hyers-Ulam stability, Rassias stability, and Ulam stability.

TL;DR: The Chebyshev pantograph operational matrix is introduced and the operational matrices of pantograph, derivative and product are utilized to reduce the problem to a set of algebraic equations.

TL;DR: In this article, a robust finite-time H∞ control problem for a class of uncertain switched neutral systems with unknown time-varying disturbance is investigated, and the uncertainties under consideration are norm bounded.

TL;DR: In this article, the stagnation point flow and heat transfer over an exponentially shrinking sheet are investigated using the boundary layer approximation and a similarity transformation in exponential form, and the governing mathematical equations are transformed into coupled, nonlinear ordinary differential equations which are then solved numerically by a shooting method with fourth order Runge-Kutta integration scheme.

TL;DR: In this article, a fractional-order terminal sliding mode controller is proposed to ensure the finite time stability of the closed-loop system subject to uncertainties, and numerical simulation results are presented and compared to illustrate the effectiveness of the proposed method.

TL;DR: A review of the literature having in mind applications and possible explanations for the use of power laws in real phenomena and some controversies around power laws are unraveled.

TL;DR: In this article, a shifted Jacobi-Gauss collocation spectral method is proposed for solving the nonlinear Lane-Emden type equation, which is based on shift Jacobi polynomials P T, n ( α, β ) (x ) with α, β ǫ ∈ (−1, ∞), T Â > 0, and n is the polynomial degree.

TL;DR: In this paper, the authors presented a method to solve nonlinear Volterra-Fredholm-Hammerstein integral equations in terms of Bernstein polynomials and operational matrix of integration together with the product operational matrix.

TL;DR: In this article, the primary resonance of a Duffing oscillator with fractional-order derivative is investigated by the averaging method, and the effect of the fractional order derivative on the system dynamics is analyzed.

TL;DR: In this article, the existence of boundary value solutions for fractional hybrid differential equations was proved under mixed Lipschitz and Caratheodory conditions under a fixed point theorem in Banach algebra due to Dhage.

TL;DR: In this paper, a hybrid prediction model with empirical mode decomposition (EMD), chaotic theory, and grey theory is constructed for short-term prediction of wind farm power, which has good prediction accuracy.