Theory and Modern Applications
Page 46 of 98
In this paper, by employing the fractional power of operators, semigroup theory, and fixed point strategy we obtain some new criteria ensuring the existence and exponential stability of a class of impulsive ne...
Recently, Jarad et al. in (Adv. Differ. Equ. 2017:247, 2017) defined a new class of nonlocal generalized fractional derivatives, called conformable fractional derivatives (CFDs), based on conformable derivatives....
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...
This paper is concerned with the fault estimation problem for a class of Takagi–Sugeno (T-S) fuzzy systems with actuator faults and sensor disturbances. Premise variables of the T-S fuzzy systems are assumed t...
In this paper, we consider a multi-term variable-order fractional diffusion equation on a finite domain, which involves the Caputo variable-order time fractional derivative of order ...
In this paper, we investigate numerical solution of the variable-order fractional Galilei advection–diffusion equation with a nonlinear source term. The suggested method is based on the shifted Legendre colloc...
In this paper, we investigate the problem of finite-time stability (FTS) of linear non-autonomous systems with time-varying delays. By constructing an appropriated function, we derive some explicit conditions in ...
This paper investigates the existence of infinitely many positive solutions for the second-order n-dimensional impulsive singular Neumann system
We deal with a nonlinear impulsive differential equation system with piecewise constant argument. We prove the existence and uniqueness of a solution. Moreover, we obtain sufficient conditions for the oscillat...
The derivation of this paper is devoted to describing the operational properties of the finite Fourier transform method, with the purpose of acquiring a sufficient theory to enable us to follow the solutions o...
Taking the delay due to the latent period of computer viruses and the delay due to the period that the anti-virus software uses to clean the computer viruses as the bifurcation parameters, local Hopf bifurcati...
In this paper, we investigate a class of boundary value problem of nonlinear Hadamard fractional differential equations with a parameter. By means of the properties of the Green function and Guo–Krasnosel’skii...
This paper addresses the stability problem of a class of switched positive nonlinear systems (SPNSs). Both continuous-time systems and discrete-time systems are studied. By applying the minimum dwell-time (MDT...
This paper uses new fractional integration operational matrices to solve a class of fractional neutral pantograph delay differential equations. A fractional-order function space is constructed where the exact ...
The periodic solution of the impulsive state feedback controls (ISFC) has been investigated extensively in the last decades. However, if the ecosystem is exploited in a period mode, what strategies are impleme...
In this paper, we derive a new generalized Volterra–Fredholm integral inequality and use it to study the dependence of solutions on the initial data for a class of fractional differential equations with Fredho...
In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker–Cusa–Huygens type.
We introduce a more general class of fractional-order boundary value problems involving non-separated type multi-point and multi-strip boundary conditions. Several existence and uniqueness results for the give...
This paper investigates the problems of robust stability and stabilization of LTI fractional-order systems with poly-topic and two-norm bounded uncertainties. Firstly, some sufficient conditions of the robust ...
In this article we investigate the existence of positive solutions for a third order nonlinear differential equation with positive and negative terms. The main tool employed here is Kiguradze’s lemma of classi...
We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fractional Boussinesq equatio...
We investigate general HIV infection models with three types of infected cells: latently infected cells, long-lived productively infected cells, and short-lived productively infected cells. We incorporate thre...
In this paper, we consider a stochastic SIR epidemic model with regime switching. The Markov semigroup theory will be employed to obtain the existence of a unique stable stationary distribution. We prove that,...
In this paper, we are concerned with asymptotic properties of solutions for a class of neutral delay differential equations with forced term, positive and negative coefficients of Euler form, and constant impu...
The Kolmogorov model has been applied to many biological and environmental problems. We are particularly interested in one of its variants, that is, a Gauss-type predator–prey model that includes the Allee eff...
In this paper, we study existence (uniqueness) of solutions for nonlinear fractional differential equations with Katugampola fractional integral conditions. Several fixed point theorems are used for sufficient...
This paper considers the problem of the simultaneous finite-time event-triggered control and fault detection for a class of continuous-time singular Markovian jump mixed delay systems (SMJDSs) under asynchrono...
This paper focuses on a certain type of periodic boundary value problems for first-order impulsive difference equations with time delay. Notions of lower and upper solutions are introduced, with which two new ...
In this paper, using the theory of q-fractional calculus, we deal with the q-Mittag-Leffler stability of q-fractional differential systems, and based on it, we analyze the direct Lyapunov method of q-fractional d...
The exact solution of fractional combined Korteweg-de Vries and modified Korteweg-de Vries (KdV–mKdV) equation is obtained by using the
In this paper, we study a new SEIRS epidemic model describing nonlinear incidence with a more general form and the transmission of influenza virus with disease resistance. The basic reproductive number
In this paper, we explore dynamic properties of a stochastic cooperation-competition model. Some sufficient conditions are established for stochastic persistence and stochastic extinction of species. Studies s...
This paper considers projective synchronization of fractional-order delayed neural networks. Sufficient conditions for projective synchronization of master–slave systems are achieved by constructing a Lyapunov...
In this article, a kind of fuzzy cellular neural networks (FCNNs) with proportional delays and leakage delays are involved. Utilizing the differential inequality strategies, a sequence of sufficient criteria e...
In this paper, the numerical stability of a partial differential equation with piecewise constant arguments is considered. Firstly, the θ-methods are applied to approximate the original equation. Secondly, the nu...
The main purpose of the paper is to extend the results of Ellerman (Int. J. Semant. Comput. 7:121–145, 2013) to the case of dynamical systems. We define the logical entropy and conditional logical entropy of fini...
In this paper, we establish a discrete-time analog for coupled within-host and between-host systems for an environmentally driven infectious disease with fast and slow two time scales by using the non-standard...
The dynamical properties of a stochastic susceptible-infected epidemic model with Logistic growth are investigated in this paper. We show that the stochastic model admits a nonnegative solution by using the Ly...
In the present paper, we find the Fourier expansion of the Apostol Frobenius–Euler polynomials. By using a Fourier expansion of the Apostol Frobenius–Euler polynomials, we derive some new and interesting results.
In this research article, a new mathematical model for the transmission dynamics of vector-borne diseases with vertical transmission and cure is developed. The non-negative solutions of the model are shown. To...
In this paper, we formulate an nonautonomous impulsive population model with nonlinear interspecific competitive terms, and introduce the random perturbation of the birth rates of two species into this model. ...
In this paper, a stochastic susceptible-infected-susceptible (SIS) epidemic model with periodic coefficients is formulated. Under the assumption that the total population is fixed by N, an analogue of the thresho...
In this work, a prey-predator model with square root response function under a state-dependent impulse is proposed. Firstly, according to the differential equation geometry theory and the method of successor f...
The robust stability for the impulsive complex-valued neural networks with mixed time delays is considered in this paper. Based on the homeomorphic mapping theorem, some sufficient conditions are proposed for ...
The present paper deals with initial value problems for the fractional evolution equations involving the Caputo fractional derivative. By deriving a property of the three-parametric Mittag–Leffler function and...
We study the global stability of endemic equilibrium of an SIS epidemic model with feedback mechanism on networks. The model was proposed by J. Zhang and J. Sun (Physica A 394:24–32, 2014), who obtained the local...
In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involving the Appell fu...
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