Theory and Modern Applications
Page 45 of 98
This paper presents a novel adaptive finite-time tracking control scheme for nonlinear systems. During the design process of control scheme, the unmodeled dynamics in nonlinear systems are taken into account. ...
In this paper, we present further generalizations of the beta function; Riemann–Liouville, Caputo and Kober–Erdelyi fractional operators by using confluent hypergeometric function with six parameters. We also ...
We investigate the long-term properties of a stochastic Lotka–Volterra model with infinite delay and Markovian chains on a finite state space. We investigate that the stochastic model admits a unique positive ...
This paper deals with the problem of estimating the unknown parameters in a long-memory process based on the maximum likelihood method. The mean-square and the almost sure convergence of these estimators based...
In this paper, a class of nonlinear fractional difference equations with Caputo-like difference operator is considered. Some existence results for the given equation are obtained by means of topological degree...
In this paper, limit cycles bifurcating from a third-order nilpotent critical point in a class of quartic planar systems are studied. With the aid of computer algebra system MAPLE, the first 12 Lyapunov consta...
In this study, we propose two techniques for clustering genetic regulatory networks with mixed delays. Laws for identifying coupling parameters are designed, and the Lyapunov theorem and Lipschitz condition ar...
This paper is devoted to establishing the existence theory for at least one solution to a coupled system of fractional order differential equations (FDEs). The problem under consideration is subjected to movab...
In this paper, we consider the stochastic Lotka–Volterra model with additive jump noises. We show some desired properties of the solution such as existence and uniqueness of positive strong solution, unique st...
This paper is concerned with the existence of entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity. Here the entire solutions are the classical solutions that exist for all
Observer design for nonlinear systems is very important in state-based stabilization, fault detection, chaos synchronization and secret communication. This paper deals with synchronization problem of a class o...
This paper investigates the existence of denumerably many positive solutions and two infinite families of positive solutions for the n-dimensional higher-order fractional differential system ...
We establish fractional integral and derivative formulas by using fractional calculus operators involving the extended generalized Mathieu series. Next, we develop their composition formulas by applying the in...
In this work, we propose a novel analytical solution approach for solving a general homogeneous time-invariant fractional initial value problem in the normal form
...We give a complete classification of all possible dynamical behavior scenarios valid in a neighborhood of non-isolated 1–1 resonant fixed points for planar maps that are real analytic. Examples from the litera...
Based on the fact that Chua’s system is a classic model system of electronic circuits, we first present modified Chua’s system with a smooth nonlinearity, described by a cubic polynomial in this paper. Then, w...
In this paper, we consider the space-fractional reaction–advection–diffusion equation with fractional diffusion and integer advection terms. By treating the first-order integer derivative as the composition of...
In this paper, we study the solution of impulsive fractional differential equations with multiple delays by using the nonlinear alternative of Leray–Schauder and the Banach fixed point method. Also, we prove t...
In this paper, the authors study the distribution of the Vasicek model with mixed-exponential jumps and its applications in finance and insurance. With the aid of the piecewise deterministic Markov process the...
In this paper, a three-species delayed food chain system with mutual interference and impulses is established. By utilizing the continuation theorem, the comparison theorem, some analysis techniques, and const...
To study the finite-time control of plasma glucose for diabetic patients with impulsive injections of insulin, we propose an impulsive differential equation model with initial and boundary conditions. The goal...
There are many natural phenomena including a crisis (such as a spate or contest) which could be described in three steps. We investigate the existence of solutions for a three step crisis integro-differential ...
The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607–2619, 2017). Depending ...
Bifurcation and chaotic behavior of a discrete-time singular bioeconomic system are investigated. First, the traditional catch equation is modified after accounting for the handling time of the catch in a sing...
The aim of this work is to establish a new fixed point theorem for generalized contraction mappings with respect to w-distances in complete metric spaces. An illustrative example is provided to advocate the usabi...
This paper is concerned with the issue of robust stability for quaternion-valued neural networks (QVNNs) with leakage, discrete and distributed delays by employing a linear matrix inequality (LMI) approach. Ba...
In this paper, we consider exponentially practical stability of a discrete time singular system with disturbance. By using Lyapunov–Krasovskii stability theory, some criteria for exponentially practical stabil...
This paper mainly considers a class of two-layer Gilpin–Ayala predator–prey models with time delays. By means of Mawhin’s continuation theorem of coincidence degree theory, some new sufficient criteria for the...
This paper deals with the existence and non-existence of the global solutions to the Cauchy problem of a semilinear parabolic equation with a gradient term. The blow-up theorems of Fujita type are established ...
In this work, an attempt is made to understand the dynamics of a modified Leslie–Gower model with nonlinear harvesting and Holling type-IV functional response. We study the model system using qualitative analy...
The main purpose of this paper is, using the elementary and combination methods, to study the arithmetical properties of the Lucas polynomials and to obtain some new and interesting identities for them.
In this paper, we investigate a class of impulsive fractional differential equations with nonlocal conditions in a Banach space. Firstly, we utilize a fixed point theorem to obtain the existence of solution. S...
In the present article, we wish to discuss q-analogues of Laplace-type integrals on diverse types of q-special functions involving Fox’s
This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we ...
In this paper, we investigate the dynamics of a time-delayed prey–predator system with θ-logistic growth. Our investigation indicates that the models based on delayed differential equations (DDEs) with and withou...
In this paper, the stability problem of a new coupled model constructed by two fractional-order differential equations for every vertex is studied. The coupled relationship is hybrid. By using the method of co...
In this paper, we propose a multi-nutrient and single microorganism chemostat model with stochastic effect and impulsive toxicant input. Firstly, for the system neglecting stochastic effect, we investigate the...
In this paper, the deterministic and stochastic eco-epidemiological models with modified Leslie–Gower functional response are studied. For a deterministic system, the stability of disease-free equilibrium and ...
This paper focuses on the state estimation problem for complex-valued memristive neural networks with time-varying delays. By utilizing Lyapunov stability theory and some matrix inequality techniques, based on...
In this paper, we consider a kind of time-varying bang–bang property of time optimal boundary controls for the heat equation. The time-varying bang–bang property in the interior domain has been considered in s...
In this paper, a single-species discrete model with stage structure is investigated. By analyzing the corresponding characteristic equations, the local asymptotic stability of non-negative equilibrium points a...
The global existence and boundedness of a reaction–diffusion–taxis system with three interacting species, among which two species consist of predators competing for one species of prey, are investigated.
In this paper, we study a class of first-order neutral differential equations with time-varying delays and coefficients. Employing the fixed point method and differential inequality techniques, easily verifiab...
This paper concerns the problem of enhanced results on robust finite time passivity for uncertain discrete time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapun...
A logistic model with impulsive Holling type-II harvesting is proposed and investigated in this paper. Here, the species is harvested at fixed moments. By using the techniques derived from the theory of impuls...
A non-selective harvesting Lotka–Volterra amensalism model incorporating partial closure for the populations is proposed and studied in this paper. Local and global stability of the boundary and interior equil...
In this paper, we investigate a fully implicit finite difference scheme for solving the time fractional advection–diffusion equation. The time fractional derivative is estimated using Caputo’s formulation, and...
We study a discrete-time model with diffusion that describe the dynamics of viral infections by using nonstandard finite difference (NSFD) scheme. The original model we considered was a viral infection model w...
In this paper, dynamic behaviors of a turbidostat model with Tissiet functional response, linear variable yield and time delay are investigated. The existence and boundedness of solutions, the local asymptotic...
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