Theory and Modern Applications
Page 66 of 98
In this paper, the formula of general solution for nonlinear systems with Caputo-Hadamard fractional derivatives and impulsive effect is found by analysis of the limit case (as impulse tends to zero), and it s...
In this paper, a new hyperchaotic complex system is presented and its dynamical properties are discussed by phase portraits, bifurcation diagrams, and the Lyapunov exponents spectra. Noticeably, based on two d...
In this study, we have simplified the Kirschner-Panetta model on the interaction of tumor cells and effector cells by considering linear growth term as opposed to logistic growth term used by Kirschner and Pan...
Based on the boundary layer function method, a class of generalized high-dimensional delayed systems in the critical case is studied. In the framework of this paper, we not only construct the asymptotic expans...
We consider a certain class of difference equations on an axis and a half-axis, and we establish a correspondence between such equations and simpler kinds of operator equations. The last operator equations can...
We investigate second order half-linear Euler type difference equations whose coefficients have mean values. We show that these equations are conditionally oscillatory and we explicitly identify the correspond...
This paper is concerned with a stage-structured predator-prey system with Holling-II functional response and two delays. Choosing a possible combination of the two delays as the bifurcation parameter, the exis...
In this paper, we discuss the existence of positive solution to singular fractional differential equations involving Caputo fractional derivative. Necessary and sufficient condition for the existence of
In the present study, keeping in view of Leslie-Gower prey-predator model, the stability and bifurcation analysis of discrete-time prey-predator system with generalized predator (i.e., predator partially dependen...
The original article was published in Advances in Difference Equations 2014 2014:165
The original article was published in Advances in Difference Equations 2014 2014:235
The time scale calculus theory can be applicable to any field in which dynamic processes are described by discrete- or continuous-time models. On the other hand, many economic models are dynamic models. Theref...
In this article, we present the existence of solutions for a higher-order coupled fractional differential equations with the Caputo fractional derivative. Our main approach is the coincidence degree theory due...
In this paper, we study the stability of sets for a class of impulsive stochastic functional differential equations. By employing piecewise continuous Lyapunov functions with Razumikhin methods, some sufficien...
We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter ϵ whose coefficients depend holomorphically on
Kim et al. (Appl. Math. Inf. Sci. 9(6):1-6, 2015) consider the q-extensions of Boole polynomials. In this paper, we consider Witt-type formula for the q-Boole polynomials with weights and derive some new interest...
In the present paper, we consider a Cauchy problem for a linear second order in time abstract differential equation with pure delay. In the absence of delay, this problem, known as the harmonic oscillator, has...
This paper is concerned with the problem of stochastic stability for a class of fuzzy Cohen-Grossberg neural networks, in which the interconnections and delays are time-varying. Based on a Lyapunov function an...
In this paper we derive new exact solitary wave solutions and quasi-periodic traveling wave solutions of the KdV-Sawada-Kotera-Ramani equation by using a method which we introduce here for the first time. Firs...
The degenerate Bernoulli polynomials were introduced by Carlitz and rediscovered later by Ustiniv under the name of Korobov polynomials of the second kind (see Carlitz in Arch. Math. (Basel) 7:28-33, 1956; Uti...
This paper deals with singular dynamical networks with non-delay coupling and unbounded time-delay coupling simultaneously, where the coupling configuration matrices are symmetric with zero row sums and nonneg...
This paper explores the numerical methods for a singular integral equation (SIE), which arise in the study of various problems of mathematical physics and engineering. The idea behind the boundary element meth...
We investigate perturbed second order Euler type half-linear differential equations with periodic coefficients and with the perturbations given by the finite sums of periodic functions which do not need to hav...
In this paper, state estimation for discrete-time BAM neural networks with time-varying delay is discussed. Under a weaker assumption on activation functions, by constructing a novel Lyapunov-Krasovskii functi...
The incomplete inverse spectral and inverse nodal problems for Dirac operator defined on a finite interval with separated boundary conditions are considered. We prove uniqueness theorems for the so-called inco...
This paper concerns the boundary value problem of a class of fractional differential equations involving the Riemann-Liouville fractional derivative with nonlocal integral boundary conditions. By using the pro...
In this paper, the authors employ Lyapunov stability theory, and the M-matrix, H-matrix, and linear matrix inequality (LMI) techniques and variational methods to obtain the LMI-based stochastically exponential ro...
In this paper, we consider the following two-point boundary value problem for q-fractional p-Laplace difference equations. New results on the existence and uniqueness of solutions for q-fractional boundary value ...
We study fractional differential equations with causal operators. The existence of solutions is obtained by applying the successive approximate method. Some applications are discussed including also the case w...
This note is motivated by some papers treating the fractional hybrid differential equations involving Riemann-Liouville differential operators of order
A discrete-time logistic model with delay is studied. The existence of a positive periodic solution for a discrete-time logistic model is obtained by a continuation theorem of coincidence degree theory, and a ...
In this paper, we establish reverse Hölder’s inequality on time scales via diamond integral, which is defined as an ‘approximate’ symmetric integral on time scales. Moreover, we give some generalizations of di...
The existence of uncountably many positive solutions and convergence of Mann iterative schemes for a fourth order neutral delay difference equation are proved. Seven examples are included.
This paper is concerned with two classes of retarded stochastic differential equations. Sufficient conditions are derived to guarantee the pth moment exponential stability and almost sure exponential stability. M...
A meshless method for the numerical solution of partial differential equations with nonlinear inequality constraints is discussed in this paper. The original nonlinear inequality problem is linearized as a seq...
By hibernating, animals can reduce their energy requirements by at least ninety percent and survive for many months while slowly catabolizing body lipid reserves. Hibernation constitutes an effective strategy ...
In this paper, we consider the logistic equation with piecewise constant argument of generalized type. We analyze the stability of the trivial fixed point and the positive fixed point after reducing the equati...
In view of Nevanlinna theory, we study the growth and poles of solutions of some complex q-difference differential equations. We obtain the estimates on the Nevalinna order, the lower order, and the counting func...
In the paper (Markechová in Fuzzy Sets Syst. 48:351-363, 1992), fuzzy dynamical systems have been defined. In this contribution, using the method of F-σ-ideals, we prove analogies of some ergodic theorems for fuz...
In this paper, we give the exponential generating functions for the generalized Fibonacci and generalized Lucas quaternions, respectively. Moreover, we give some new formulas for binomial sums of these quatern...
The main aim of this paper is to develop four innovative linearization formulas for some nonsymmetric Jacobi polynomials. This means that we find the coefficients of the products of Jacobi polynomials of certa...
A discrete tuberculosis model with direct progression and treatment of latently infected individuals is presented. The model does not consider the drug-resistant TB, and it assumes that latently infected indiv...
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