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Showing papers in "Communications in Nonlinear Science and Numerical Simulation in 2018"


Journal ArticleDOI
TL;DR: This review article aims to present some short summaries written by distinguished researchers in the field of fractional calculus that will guide young researchers and help newcomers to see some of the main real-world applications and gain an understanding of this powerful mathematical tool.

922 citations


Journal ArticleDOI
TL;DR: In this article, a new fractional derivative with respect to another function is introduced, the so-called ψ-Hilfer fractional derivatives, which can be used to obtain uniformly convergent sequence of function, uniformly continuous function and examples including the Mittag-Leffler function with one parameter.

485 citations


Journal ArticleDOI
TL;DR: The results show that the potential barrier is a key factor to determine the orbit height of high-energy interwell oscillations, which influences the amplitude of the output voltage in asymmetric tristable energy harvesters.

345 citations


Journal ArticleDOI
TL;DR: A new formula for the fractional derivative with Mittag-Leffler kernel is established, in the form of a series of Riemann–Liouville fractional integrals, which brings out more clearly the non-locality of fractional derivatives and is easier to handle for certain computational purposes.

246 citations


Journal ArticleDOI
TL;DR: By introducing an ideal and active flux-controlled memristor into an existing hypogenetic chaotic jerk system, an interesting Memristor-based chaotic system with hypogenetics jerk equation and circuit forms is proposed, which exhibits the extreme multistability phenomenon of coexisting infinitely many attractors.

217 citations


Journal ArticleDOI
TL;DR: The Prabhakar function, a three parameter Mittag–Leffler function, is investigated and the asymptotic expansion for large arguments is investigated in the whole complex plane and, with major emphasis, along the negative semi-axis.

175 citations


Journal ArticleDOI
TL;DR: It is proved that the conformable fractional derivative, the M-fractional derivative), the alternative fractional derivatives, the local fractionsal derivative and the Caputo–Fabrizio fractional derived with exponential kernels cannot be considered as fractionalderived of non-integer orders.

159 citations


Journal ArticleDOI
TL;DR: A modification of the classical fractional Maxwell model is proposed, in which the Caputo derivative is replaced with the Prabhakar one, in order to recover a formal equivalence between the new model and the known classical models of linear viscoelasticity.

143 citations


Journal ArticleDOI
TL;DR: By designing a simple linear feedback controller, the finite-time synchronization criterion for drive-response MFFCNN systems is derived according to the definition of finite- time synchronization.

109 citations


Journal ArticleDOI
Zixiang Zhou1
TL;DR: It is shown that the solutions of the nonlocal derivative nonlinear Schrodinger equation can be globally defined and bounded for all (x, t) if the eigenvalues and the parameters characterizing the ratio of the two entries of the solutionsof the Lax pair are chosen properly.

108 citations


Journal ArticleDOI
TL;DR: Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative are investigated.

Journal ArticleDOI
TL;DR: The nonlinear supercritical parametric dynamics of a Timoshenko microbeam subject to an axial harmonic excitation force is examined theoretically and theoretically by means of different numerical techniques, and employing a high-dimensional analysis.

Journal ArticleDOI
TL;DR: It is verified that the Caputo–Fabrizio operator does not fit the usual concepts neither for fractional nor for integer derivative/integral.

Journal ArticleDOI
TL;DR: A stochastic single species model with Allee effect under regime switching is developed and it is indicated that the regime switching can suppress the extinction of the species.

Journal ArticleDOI
TL;DR: Some general restrictions that can be imposed on the structure and properties of dynamic memory are described and a generalization of the Harrod–Domar model, where the power-law memory is taken into account, is considered.

Journal ArticleDOI
TL;DR: The main physical implication of the results is that both momentum and temperature layers are thinned with strong magnetic fields, and upper branch solutions are more cooled leading to higher heat transfer rates as compared to the lower branches.

Journal ArticleDOI
TL;DR: The obtained results indicate the high performance in terms of execution-time and security level of the proposed cipher algorithm, and validate its robustness against cryptographic attacks, and hence confirm its efficiency for real-time secure image transmission.

Journal ArticleDOI
TL;DR: Finite-time stability of Caputo delta fractional difference equations is investigated using a generalized Gronwall inequality on a finite time domain and finite-time stable conditions are provided.

Journal ArticleDOI
TL;DR: It is revealed that the stability and bifurcation of high-dimension fractional ring-structured neural networks with multiple time delays heavily relies on the sum of time delays for the proposed networks, and the stability performance of such networks can be markedly improved by selecting carefully the total time delays.

Journal ArticleDOI
TL;DR: A new computational method is proposed to solve a class of nonlinear stochastic differential equations (SDEs) driven by fractional Brownian motion, based on a new class of orthogonal wavelets, namely the Chebyshev cardinal wavelets.

Journal ArticleDOI
TL;DR: This paper introduces the central-point triangular whitenization weight function in state division to calculate possibilities of research values in each state which reflect preference degrees in different states in an objective way and verifies this model's validity by comparing with GM(1,1) based on background value optimization and the traditional Grey-Markov forecasting model.

Journal ArticleDOI
TL;DR: This work establishes that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario, and proposes an explicit finite-difference discretization of the authors' fractional model based on the use of fractional centered differences.

Journal ArticleDOI
TL;DR: The results show that rogue waves can come from the extreme behavior of the breather solitary waves for the (2+1)-dimensional gCHKP equation.

Journal ArticleDOI
TL;DR: The conditions for the modulational instability of plane-wave solutions of the integrable three-component nonlinear Schrodinger equations are found and the general formulae for the N th-order vector rational and semi-rational rogue wave solutions are presented by the generalized Darboux transformation and formal series method.

Journal ArticleDOI
TL;DR: A universal approach is described for evaluating main characteristics of the resonant particle dynamics: probability of trapping into resonance, energy change due to scattering and trapping, and stability of trapped motion and evolution of particle ensemble in systems with trapping.

Journal ArticleDOI
TL;DR: This paper investigates the cluster synchronization of complex dynamical networks consisted of identical or nonidentical Lur’e systems and designs randomly occurring adaptive pinning controllers with two independent Bernoulli stochastic variables, based on an extended integral inequality, the convex combination theorem and S-procedure.

Journal ArticleDOI
TL;DR: A new relaxed integral inequality is developed to reduce the estimation gap of popular Wirtinger-based inequality (WBI) and show the advantages of the proposed inequality over several existing inequalities that also improve the WBI.

Journal ArticleDOI
TL;DR: The ( 3 + 1 ) -dimensional KP–Boussinesq equation, which can be used to describe the nonlinear dynamic behavior in scientific and engineering applications, is investigated and general high–order soliton solutions are derived by using the Hirota’s bilinear method combined with the perturbation expansion technique.

Journal ArticleDOI
TL;DR: This work proposes a closed formula for the ( n + ν ) –order fractional derivative of the Gaussian function, based on the Caputo–Fabrizio definition, as an approach for analysing those attributes.

Journal ArticleDOI
TL;DR: This paper studies the efficient solution of the nonlinear Schrodinger equation with wave operator, subject to periodic boundary conditions, by means of energy-conserving methods in the HBVM class (Hamiltonian boundary value methods).