Theory and Modern Applications
Page 24 of 98
In this paper, we propose a simple network consisting of only two nodes and two paths. The first node, which is called the source, has three competing firms that send their quantities of load via the two paths...
Fractional difference equations have become important due to their qualitative properties and applications in discrete modeling. Stability analysis of solutions is one of the most widely used qualitative prope...
The primary objective of this research paper is to investigate two kinds of high-order tempered fractional differential equations integral boundary value problems. By means of the mixed monotone operators fixe...
In this paper, we use the Hirota bilinear method for investigating the third-order evolution equation to determining the soliton-type solutions. The M lump solutions along with different types of graphs including...
A stochastic susceptible–exposed–infected–recovered (SEIR) model with nonlinear incidence rate is investigated. Under suitable conditions, existence and uniqueness of a global solution, stationary distribution...
The economic order quantity (EOQ) is the order quantity that minimizes the total holding costs and ordering costs. In this effort, we propose a design for EOQ by employing a conformable differential-difference...
We show the global structure of the set of positive solutions of a discrete Dirichlet problem involving the p-Laplacian difference operator suggesting suitable conditions on the weight function and nonlinearity. ...
The aim of this work is to develop a novel explicit unconditionally positivity preserving finite difference (FD) scheme and an implicit positive FD scheme for the numerical solution of dengue epidemic reaction...
This work is concerned with the oscillatory behavior of solutions of fourth-order neutral differential equations. By using the Riccati transformation and integral averaging techniques we obtain some new Kamene...
The present article addresses the exponential stability of recurrent neural networks (RNNs) with distributive and discrete asynchronous time-varying delays. Some novel algebraic conditions are obtained to ensu...
Conventional non-negative algorithms restrict the weight coefficient vector under non-negativity constraints to satisfy several inherent characteristics of a specific system. However, the presence of impulsive...
In this paper, we show a zero-Hopf bifurcation in a four-dimensional smooth quadratic autonomous hyperchaotic system. Using averaging theory, we prove the existence of periodic orbits bifurcating from the zero...
In this article, the first part is concerned with the important questions related to the existence and uniqueness of solutions for nonlinear reaction-diffusion systems. Secondly, an efficient positivity-preser...
In this paper, we consider a predator–prey metapopulation model with a ring-structured configuration of an arbitrary and finite number of patches. The prey are assumed to disperse between the connected patches...
This paper investigates the Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation by using Hirota’s direct method and the Kadomtsev–Petviashvili (KP) hierarchy reduction method. Soliton solutions in the Grammia...
In this paper, we investigate the degenerate Hopf bifurcation of a Leslie–Gower predator–prey system with predator harvest. The known work discussed the Hopf bifurcation of this system when the first Lyapunov ...
In the paper, the authors consider a ratio of finite many gamma functions and find its monotonicity properties such as complete monotonicity, the Bernstein function property, and logarithmically complete monot...
In this paper, we give some direct approximation results by modified Kantorovich–Szász type operators involving Charlier polynomials. Further, approximation results are also developed in polynomial weighted sp...
The present paper focuses on the chirped soliton solutions of the Fokas–Lenells equation in the presence of perturbation terms. A complex envelope traveling-wave solution is used to reduce the governing equati...
In many areas, researchers might think that a differential equation model is required, but one might be forced to use an approximate difference equation model if data is only available at discrete points in ti...
In this paper, a stochastic space fractional advection diffusion equation of Itô type with one-dimensional white noise process is presented. The fractional derivative is defined in the sense of Caputo. A stoch...
In this paper, we consider the optimal control problem for fully coupled forward–backward stochastic difference equations of mean-field type under weak convexity assumption. By virtue of employing a suitable p...
The paper addresses the optimal control and stabilization problems for the indefinite discrete-time mean-field system over infinite horizon. Firstly, we show the convergence of the generalized algebraic Riccat...
We consider two models of fractional calculus which are defined using three-parameter Mittag-Leffler functions: the Prabhakar definition and a recently defined extension of the Atangana–Baleanu definition. By ...
A new auxiliary result based on a three step quadratic kernel utilizing the concepts of local fractional calculus is obtained. Using this new auxiliary result we have several new Newton type inequalities whose...
In this paper, we study the rubella disease model with the Caputo–Fabrizio fractional derivative. The mathematical solution of the liver model is presented by a three-step Adams–Bashforth scheme. The existence...
In this study, we are currently investigating the controllability of nonlinear fractional differential control systems with delays in the state function. The solution representations of fractional delay differ...
In this work, we analyze and test a local discontinuous Galerkin method for solving the Burgers-type equation. The proposed numerical method, which is high-order accurate, is based on a finite difference schem...
The Editors-in-Chief have retracted this article [1] because it overlaps with articles by other authors that were simultaneously under consideration at different journals [2,3].
The original article was published in Advances in Difference Equations 2017 2017:87
A system of linear Riemann–Liouville fractional differential equations with constant delay is studied. The initial condition is set up similar to the case of the ordinary derivative. Explicit formulas for the ...
In this paper, we use an Ornstein–Uhlenbeck process to describe the environmental stochasticity and propose a stochastic predator–prey model with modified Leslie–Gower and Holling-type II schemes. For each spe...
This note is concerned with establishing existence theory of solutions to a class of implicit fractional differential equations (FODEs) involving nonsingular derivative. By using usual classical fixed point th...
The primary purpose of this study is to perform the comparison of deterministic and stochastic modeling. The effect of threshold number is also observed in this model. For numerical simulations, we have develo...
This article presents a numerical algorithm for solving time fractional Burgers’ and Fisher’s equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the...
A new solution for fractional extended Fisher–Kolmogorov (FEFK) equation using the q-homotopy analysis transform method (q-HATM) is obtained. The fractional derivative considered in the present work is developed ...
The stochastic research and development (R&D) model plays an important role in economic growth theories. To explain the growth performance of the economy under regime switching, we first establish sufficient c...
In this paper, we propose an efficient B-spline finite element method for a class of fourth order nonlinear differential equations with variable coefficient. For the temporal discretization, we choose the Cran...
The Correction to this article has been published in Advances in Difference Equations 2020 2020:371
In this paper, our main purpose is to present an analytical solution for measles spread model with three doses of vaccination using Caputo–Fabrizio fractional derivative (CFFD). The presented solution is based...
This paper employs an efficient technique, namely q-homotopy analysis transform method, to study a nonlinear coupled system of equations with Caputo fractional-time derivative. The nonlinear fractional coupled...
The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithm functions. Recently, the type 2 poly-Bernoulli numbers and polynomials were defined by means of ...
This work mainly investigates the separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio fractional derivatives. An inequality ensuring the positivity of the fractional derivative...
In this paper, we consider the effects of the small and abrupt random perturbations in the environment, and formulate a stochastic single species model with Allee effect and jump-diffusion. We first prove that...
This research investigates the bounds of fractional integral operators containing an extended generalized Mittag-Leffler function as a kernel via several kinds of convexity. In particular, the established boun...
In this work, the semi-analytical solution is studied for the diffusive logistic equation with both mixed instantaneous and delayed density. The domain of reaction–diffusion in one dimension is shown. Delay pa...
In this paper, we investigate the existence of solutions for two nonlinear fractional multi-term integro-differential inclusions in two hybrid and non-hybrid versions. The boundary value conditions are in the ...
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