Theory and Modern Applications
Page 54 of 98
This paper focuses on a three-species food chain system which is formulated as stochastic differential equations with regime switching represented by a hidden Markov chain. Firstly, using the Wonham filter, we...
The purpose of this paper is to study the solvability of a resonant boundary value problem for the fractional p-Laplacian equation. By using the continuation theorem of coincidence degree theory, we obtain a new ...
The multilevel augmentation method with the anti-derivatives of the Daubechies wavelets is presented for solving nonlinear two-point boundary value problems. The anti-derivatives of the Daubechies wavelets are...
We propose a new method called the fractional reduced differential transform method (FRDTM) to solve nonlinear fractional partial differential equations such as the space-time fractional Burgers equations and ...
This paper is concerned with near-optimality for stochastic control problems of linear delay systems with convex control domain and controlled diffusion. Necessary and sufficient conditions for a control to be...
In this paper, we propose a new three-level implicit method based on a half-step spline in compression method of order two in time and order four in space for the solution of one-space dimensional quasi-linear...
Synchronization of chaotic systems which is defined based on the exponential stability for encrypts of signals is presented in this paper. An adaptive control scheme is proposed, and the convergence of the syn...
In this paper, we give improved results on the existence of positive solutions for the following one-dimensional p-Laplacian equation with nonlinear boundary conditions:
In the study of pattern formation in bi-stable systems, the extended Fisher-Kolmogorov (EFK) equation plays an important role. In this paper, a Fourier pseudo-spectral method for solving the EFK equation in tw...
The rodent is one important component of an ecosystem; however, abundance of rodents may have negative effects to humans. Based on a seasonally breeding model and the logistic model, the effect of impulse leth...
In this paper, we study the HIV infection model based on fractional derivative with particular focus on the degree of T-cell depletion that can be caused by viral cytopathicity. The arbitrary order of the frac...
Sharp sufficient conditions for the solvability of the Cauchy problem for linear singular functional differential equations are obtained.
In this paper, we investigate the topological structure for the solution set of Caputo type neutral fractional stochastic evolution inclusions in Hilbert spaces. We introduce the concept of mild solutions for ...
Measles remain to be an important global public health issue in China. In spite of large coverage rates of the first dose of Measles mumps rubella (MMR) combination vaccines (MMR1), large numbers of measles ca...
The key purpose of the present work is to examine a fractional giving up smoking model pertaining to a new fractional derivative with non-singular kernel. The numerical simulations are conducted with the aid o...
Exploring some results of Wang et al. (Adv. Differ. Equ. 2016:33, 2016) from another point of view, we first investigate the stability and direction for a class of Schrödingerean difference equations with Schrödi...
The Retraction Note to this article has been published in Advances in Difference Equations 2020 2020:181
This article shows epidemic model, earlier suggested in ordinary differential equation philosophy, can be extended to fractional order on a reliable agenda of biological comportment. A set of domains for the m...
The Retraction Note to this article has been published in Advances in Difference Equations 2021 2021:114
In this study we propose a hybrid spectral exponential Chebyshev method (HSECM) for solving time-fractional coupled Burgers equations (TFCBEs). The method is based upon a spectral collection method, utilizing ...
This paper proposes the robust iterative learning control (ILC) design for uncertain linear systems with time-varying delays and random packet dropouts. The packet dropout is modeled by an arbitrary stochastic...
In this paper, we investigate the existence and uniqueness of S-asymptotically ω-periodic solutions to fractional differential equations of order
In this work, we study a boundary value problem for a fractional q-difference equation. By using the monotone iterative technique and lower-upper solution method, we get the existence of positive or negative solu...
We give a representation of the class of Cullen-regular functions in split-quaternions. We consider each Cullen’s form of split-quaternions, which provides corresponding Cauchy-Riemann equations for split-quat...
In this paper, we propose a fractional order epidemic model for obesity contagion. The population size is assumed to be nonconstant, which is more realistic. The model considers vertical transmission of obesit...
The aim of this paper is to study the generalized Hyers-Ulam stability of a form of reciprocal-cubic and reciprocal-quartic functional equations in non-Archimedean fields. Some related examples for the singula...
This paper is concerned with some dynamics of the permanent-magnet synchronous motor chaotic system based on Lyapunov stability theory and optimization theory. The innovation of the paper lies in that we deriv...
In this article, we investigate some uniqueness and Ulam’s type stability concepts for the Darboux problem of partial functional differential equations with noninstantaneous impulses and delay in Banach spaces...
This paper mainly focuses on a fractional model for unsteady-state fluid flow problem developed based on the meshless local Petrov-Galerkin (MLPG) method with the moving kriging (MK) technique as a background....
Herein, an innovative operational matrix of fractional-order derivatives (sensu Caputo) of Fermat polynomials is presented. This matrix is used for solving the fractional Bagley-Torvik equation with the aid of ta...
This paper is concerned with asymptotic and oscillatory properties of the nonlinear third-order differential equation with a negative middle term. Both delay and advanced cases of argument deviation are consid...
In this paper we show a connection between Levin-Nohel integro-differential equations and ordinary functional differential equations. Based on this connection, we obtain several new conditions for the stabilit...
In this paper, we apply the classical control theory to a fractional differential system in a bounded domain. The fractional optimal control problem (FOCP) for differential system with time delay is considered...
This work presents the homotopy perturbation transform method for nonlinear fractional partial differential equations of the Caputo-Fabrizio fractional operator. Perturbative expansion polynomials are consider...
This paper addresses a class of fractional stochastic impulsive neutral functional differential equations with infinite delay which arise from many practical applications such as viscoelasticity and electroche...
The goal of this paper is to study the stability and traveling waves of stage-structured predator-prey reaction-diffusion systems of Beddington-DeAngelis functional response with both nonlocal delays and harve...
We discuss a new nine-point fourth-order and five-point second-order accurate finite-difference scheme for the numerical solution of two-space dimensional convection-diffusion problems. The compact operators a...
In this paper, we study anti-periodic boundary value problems for systems of generalized Sturm-Liouville and Langevin fractional differential equations. Existence and uniqueness results are proved via fixed po...
This paper is concerned with fuzzy bidirectional associative memory (BAM) Cohen-Grossberg neural networks with mixed delays and impulses. By constructing an appropriate Lyapunov function and a new differential...
We study the nonexistence of (nontrivial) global solutions for a class of fractional integro-differential problems in an appropriate underlying space. Integral conditions on the kernel, and for some degrees of...
This paper investigates the long time behavior of tumor cells evolution in a tumor-immune system competition model perturbed by environmental noise. Sufficient conditions for extinction, stochastic persistence...
In this paper, a general neutral stochastic functional differential equations with infinite delay and Lévy jumps (NSFDEwLJs) is studied. We investigate the existence and uniqueness of solutions to NSFDEwLJs at...
In this paper, the existence of local and global Hopf bifurcation for a delay commodity market model is studied in detail. As time delay increases, the commodity price will fluctuate periodically. Furthermore,...
In this paper, we study a class of nonlinear multiple base points impulsive fractional differential equations involving the three-point boundary conditions. A new result on the existence of a solution is estab...
This study is concerned with the problem of finite-time state estimation for T-S fuzzy stochastic jumping neural networks, where the communication links between the stochastic jumping neural networks and its e...
The paper develops a derivative-type (D-type) networked iterative learning control (NILC) scheme for repetitive discrete-time systems with packet dropouts stochastically occurred in input and output communicat...
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