Theory and Modern Applications
Page 40 of 98
In this paper, starting from a fixed δ-sequence, we use the generalized Taylor’s formula based on conformable derivatives and the neutrix limit to find the powers of the Dirac delta function ...
The fractional reaction–subdiffusion equation is one of the most famous subdiffusion equations. These equations are widely used in recent years to simulate many physical phenomena. In this paper, we consider a...
In the paper, the conservative Fourier spectral scheme is presented for the coupled Schrödinger–Boussinesq equations. We apply the Fourier collocation scheme to spatial derivatives and the Crank–Nicolson schem...
In this paper, the existence and exponential stability of mild solutions of random impulsive fractional differential equations are studied. The results are obtained by using the Leray–Schauder alternative fixe...
This paper is devoted to the oscillatory problem in the fractional-order delay differential equations. First, we prove the convergence of the Laplace transform of a fractional operator by the generalized Gronw...
In this paper, we study a discrete predator–prey system with modified Holling–Tanner functional response. We derive conditions of existence for flip bifurcations and Hopf bifurcations by using the center manif...
In this paper, we investigate the dynamics of a nonlinear differential system, a mathematical model of the coupled hematopoiesis network. The asymptotic stability of a unique positive periodic solution of the ...
This paper is devoted to study the permanence and periodic solution of a competitive system with infinite delay, feedback control, and the Allee effect. We derive sufficient conditions for the permanence and e...
We study evolution inclusions given by multivalued perturbations of m-dissipative operators with nonlocal initial conditions. We prove the existence of solutions. The commonly used Lipschitz hypothesis for the...
In the publication of this article [1], there is an error in one of the authors’ name. This has now been included in this correction.
The original article was published in Advances in Difference Equations 2018 2018:274
The aim of this paper is using an elementary method and the properties of the Bernoulli polynomials to establish a close relationship between the Euler numbers of the second kind ...
Applying the z-transform method, we study the Ulam stability of linear difference equations with constant coefficients. To a certain extent, our results can be viewed as an important complement to the existing me...
In this paper, we study a new boundary value problem of arbitrary order fractional differential equations equipped with new integro-multipoint boundary conditions. Existence and uniqueness results for the give...
In this research article, we focus on the system of linear Volterra fuzzy integro-differential equations and we propose a numerical scheme using the variational iteration method (VIM) to get a successive appro...
In this paper we study random non-autonomous second order linear differential equations by taking advantage of the powerful theory of random difference equations. The coefficients are assumed to be stochastic ...
In the process of rumor spreading, controlling and killing rumor problem is of great importance on social networks. In this paper, we present a new SEIR (susceptible-exposed-infected-removed) rumor spreading mode...
This paper presents a multicontroller structure for an SEIADR (susceptible-exposed-symptomatic infectious-asymptomatic infectious-dead lying bodies recovered by immunity, or immune, subpopulations) epidemic mo...
According to the principle of conservation of mass and the fractional Fick’s law, a new two-sided space-fractional diffusion equation was obtained. In this paper, we present two accurate and efficient numerica...
This paper is a continuation of the work (Lastra and Malek in J. Differ. Equ. 259(10):5220–5270, 2015) where singularly perturbed nonlinear PDEs have been studied from an asymptotic point of view. Here, the parti...
In this paper, we discuss the existence and uniqueness of solutions for two new classes of sequential fractional differential equations of Riemann–Liouville and Caputo types with generalized fractional integra...
In this work, we consider a water eutrophication model with impulsive dredging. We prove that all solutions of the investigated system are uniformly bounded. There exists globally asymptotically stable periodi...
In this paper, finite-time synchronization problems for a class of nonlinear coupled Markovian jump delay time complex networks (NCMJDTCNs) with stochastic noises and a class of linear coupled Markovian jump d...
We investigate a singular fractional differential equation with an infinite-point fractional boundary condition, where the nonlinearity
In this article, we first create a new comparison principle for a nonlinear impulsive boundary problem involving different deviating arguments. Then we employ the new result and iterative method to study the e...
In this paper,we are interested in the existence and uniqueness of positive solutions for integral boundary value problem with fractional q-derivative:
...In this article, we discuss a new two-level implicit scheme of order of accuracy two in time and four in space based on the spline in compression approximations for the numerical solution of 1D unsteady quasi-...
We apply the concept of measure of noncompactness to study the existence of solution of second order differential equations with initial conditions in the sequence space
...
Recently, distributed convex optimization using a multiagent system has received much attention by many researchers. This problem is frequently approached by combing the consensus algorithms in the multiagent ...
This paper is concerned with the approximate controllability and complete controllability of semilinear fractional functional differential systems with control involving Caputo fractional derivative. By using ...
This paper deals with a predator–prey model with both species in the delayed-dispersal case in a two-patch environment. The purpose of this paper is to study the effect of two dispersal delays on the stability...
Most stochastic age-dependent capital systems cannot be solved explicitly, so it is necessary to develop numerical methods and study the properties of numerical solutions. In this paper, we consider a class of...
In this paper, using the topological degree theory, we establish two existence theorems for nontrivial solutions for boundary value problems of a fourth order difference equation with a sign-changing nonlinear...
This paper deals with some existence results for two classes of coupled systems of Hilfer and Hilfer–Hadamard random fractional differential equations. The main tool used to carry out our results is Itoh’s ran...
The paper is devoted to an investigation of the existence of a positive periodic solution for a kind of fourth-order singular Rayleigh equation with time-dependent deviating argument, where the nonlinear term g s...
Allee effect (i.e. sparse effect) is active when the population density is small. Our purpose is to study such an effect of this phenomenon on population dynamics. We investigate an impulsive state feedback co...
This paper considers a portfolio selection problem with a quadratic utility of consumption, which is symmetric with respect to a bliss point. At bliss point, the utility function has its maximum value and furt...
In the present study, by employing differential inequality theory, some novel assertions are gained to validate the global exponential convergence on neutral type shunting inhibitory cellular neural networks i...
In this paper, a novel stage-structured single population model with state-dependent maturity delay is formulated and analyzed. The delay is related to the size of population and taken as a non-decreasing diff...
Based on the locally one-dimensional strategy, we propose two high order finite difference schemes for solving two-dimensional linear parabolic equations. In the first method, fourth order approximation in spa...
The purpose of this paper is to investigate the existence and uniqueness of nonnegative solutions for Langevin equations with two fractional orders:
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