Theory and Modern Applications
Page 36 of 98
In this paper, we establish some Lyapunov-type inequalities for a class of linear and nonlinear fractional q-difference boundary value problems under Cauchy boundary conditions. As applications, we use the inequa...
In this paper, we give an affirmative answer to the following question: Is the solvability of some nonlinear dynamic equations on a time scale
In this article, we study a coupled system of singular fractional difference equations with fractional sum boundary conditions. A sufficient condition of the existence of positive solutions is established by e...
In this paper, we present a semi-analytic method called the local fractional homotopy analysis method (LFHAM) for solving differential equations involving local fractional derivatives based on the local fracti...
In this paper, the bifurcations of a modified Degasperis–Procesi equation are studied under different parametric conditions, which have not been investigated by the bifurcation theory of dynamical systems befo...
In this paper, we study the existence of solutions for hybrid fractional differential equations involving fractional Caputo derivative of order
In this paper, bifurcation analysis of a discrete Hindmarsh–Rose model is carried out in the plane. This paper shows that the model undergoes a flip bifurcation, a Neimark–Sacker bifurcation, and
This paper is concerned with the stability criteria for a discrete-time linear system with interval time-varying delays. By using the time delay division we construct an augmented Lyapunov–Krasovskii functiona...
In this paper, we propose a fractional form of a new three-dimensional generalized Hénon map and study the existence of chaos and its control. Using bifurcation diagrams, phase portraits and Lyapunov exponents...
This paper investigates the problem of a state bounding estimation for a linear continuous-time singular system with time-varying delay. By employing the maximal Lyapunov–Krasovskii functional and applying the...
This paper is concerned with a class of anti-periodic boundary value problems for fractional differential equations with the Riesz–Caputo derivative, which can reflected both the past and the future nonlocal m...
Pesticides often cause residual and delayed effects on pests. Considering these effects, we use a pollution emission model to simulate the process of spraying pesticides. Many pests reproduce only at a fixed t...
Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and c...
A new approximate technique is introduced to find a solution of FVFIDE with mixed boundary conditions. This paper started from the meaning of Caputo fractional differential operator. The fractional derivatives...
In this note, we will show that an entire function is equal to its difference operator if it has a growth property and shares a set, where the set consists of two entire functions of smaller orders. This result g...
In this paper, we study the Legendre spectral element method for solving the sine-Gordon equation in one dimension. Firstly, we discretize the equation by Legendre spectral element in space and then discretize...
In this article, multiple positive solutions are considered for nonlinear mixed fractional differential equations with a p-Laplacian operator. Using the Avery–Peterson fixed point theorem, we conclude to the exis...
Under the assumption that stochastic white noise perturbations are directly proportional to the deviation of the state from the equilibrium states of a continuous mutualistic model, we use the Euler–Maruyama d...
The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials. As a generalization of this, we ...
In this paper, we propose a nonlocal diffusion infectious disease model with nonlinear incidences and distributed delay to model the transmission of the epidemic. By a fixed point theorem and a limiting argume...
This paper studied the existence and uniqueness of the solution of the fractional logistic differential equation using Hadamard derivative and integral. Previous work has shown that there is not an exact solut...
In this paper, a Kaldor–Kalecki model of business cycle with two discrete time delays is considered. Firstly, by analyzing the corresponding characteristic equations, the local stability of the positive equili...
In this article, we consider a study of a general class of nonlinear singular fractional DEs with p-Laplacian for the existence and uniqueness (EU) of a positive solution and the Hyers–Ulam (HU) stability. To pro...
This paper introduces the solution of differential algebraic equations using two hybrid classes and their twin one-leg with improved stability properties. Physical systems of interest in control theory are som...
We consider the multiplicity of positive solutions (PSs) for a coupled system involving nonlinear impulsive fractional differential equations with parameters. By employing the classical Guo–Krasnosel’skii fixe...
In this paper, we study a coupled system of implicit impulsive boundary value problems (IBVPs) of fractional differential equations (FODEs). We use the Schaefer fixed point and Banach contraction theorems to o...
In this paper, by using the least action principle, an existence result of nontrivial weak solutions for a class of fractional impulsive coupled systems with
...
We analyze the stability of positive equilibrium in a predator-prey model with time delay Ï„ and subsidies. The sufficient conditions of the local Hopf bifurcations at the positive equilibrium are obtained. By cen...
A higher-order blended compact difference (BCD) scheme is proposed to solve the general two-dimensional (2D) linear second-order partial differential equation. The distinguishing feature of the present method ...
We solve a coupled system of nonlinear fractional differential equations equipped with coupled fractional nonlocal non-separated boundary conditions by using the Banach contraction principle and the Leray–Scha...
The economic order quantity (EOQ) model describes the quantity that minimizes the aggregate sum of all cost functions. We propose an assembly for EOQ, nonlinear local fractional differential models with costs ...
A powerful analytical approach, namely the fractional residual power series method (FRPS), is applied successfully in this work to solving a class of fractional stiff systems. The methodology of the FRPS metho...
We introduce nonlinear fractional BVPs including a generalized proportional derivatives with nonlocal multipoint and substrip boundary conditions. The nonlinearities are defined on the Orlicz space and depend ...
Throughout this article, the conundrum on finite-time cluster synchronization is investigated for time-varying delayed complex dynamical networks using a kind of new hybrid control scheme. In the light of Lyap...
In this paper, the dynamical behaviors of a discrete-time prey–predator model with Allee effect on the prey population are investigated. The existence and topological classification of the fixed points of the ...
The linear estimation (or optimal control) problem in the emerging area of time-delay systems, multiplicative noise systems, and Markov jump linear systems has been taken into consideration by the control engi...
New exact solutions of the space–time conformable Caudrey–Dodd–Gibbon (CDG) equation have been derived by implementing the conformable derivative. The generalized Riccati equation mapping method is applied to ...
In this paper, by applying Kronecker product and vectorization operator, we extend two mathematical equivalent forms of the conjugate residual squared (CRS) method to solve the periodic Sylvester matrix equati...
In this paper, we define a characteristic equation of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative. At the same time, by applying the Laplace transform and matrix ...
In this paper, we consider a nonlocal boundary value problem of nonlinear implicit fractional Langevin equation with noninstantaneous impulses. We study the existence, uniqueness and generalized Ulam–Hyers–Ras...
In this paper, we consider the linear finite volume method (FVM) for the stochastic Helmholtz equation, driven by white noise perturbed forcing terms in one-dimension. We first deduce the linear FVM for the de...
It was found that the constitutive behaviour of granular soil was dependent on its density and pressure (i.e. material state). To capture such state dependence, a variety of state variables were empirically pr...
By using stochastic analysis, fractional analysis, compact semigroups and the Schauder fixed-point theorem, we discuss the approximate boundary controllability of a nonlocal Hilfer fractional stochastic differ...
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