Articles

An asymmetric information non-zero sum differential game of mean-field backward stochastic differential equation with applications

This paper is concerned with a kind of non-zero sum differential game driven by mean-field backward stochastic differential equation (MF-BSDE) with asymmetric information, whose novel feature is that both the ...

Authors: Pengyan Huang, Guangchen Wang and Huanjun Zhang

Dynamics analysis of a stochastic non-autonomous one-predator–two-prey system with Beddington–DeAngelis functional response and impulsive perturbations

In this paper, we explore a stochastic non-autonomous one-predator–two-prey system with Beddington–DeAngelis functional response and impulsive perturbations. First, by using Itô’s formula, exponential martinga...

Authors: Haokun Qi, Xinzhu Meng and Tao Feng

Computable solution of fractional kinetic equations using Mathieu-type series

The Mathieu series appeared in the study of elasticity of solid bodies in the work of Émile Leonard Mathieu. Since then numerous authors have studied various problems arising from the Mathieu series in several...

Authors: Owais Khan, Nabiullah Khan, Dumitru Baleanu and Kottakkaran Sooppy Nisar

Oscillations of differential equations with non-monotone deviating arguments

The oscillatory behavior of the solutions to a differential equation with several non-monotone arguments and nonnegative coefficients is studied, and some new oscillation criteria are given. More precisely, su...

Authors: George E. Chatzarakis, Irena Jadlovská and Tongxing Li

Dynamical modeling of the control of brown planthoppers by Beauveria bassiana and Cyrtorhinus lividipennis

In this work, the control of brown planthopper, a major pest of rice, when a biological control agent (Cyrtorhinus lividipennis) and a pathogen (Beauveria bassiana) are utilized is investigated mathematically. An...

Authors: Chontita Rattanakul

Exponentially stable solution of mathematical model of agents dynamics on time scales

This work is an attempt at studying leader-following model on the arbitrary time scale. The step size is treated as a function of time. Our purpose is establishing conditions ensuring a leader-following consen...

Authors: Ewa Schmeidel, Urszula Ostaszewska and Małgorzata Zdanowicz

Two ways for solving a class of rational second-order difference equations

We consider a class of second-order rational difference equations with two parameters, and we show, in two ways, that the class of equations is solvable in closed form. One way is based on using an invariant f...

Authors: Stevo Stević

Mixed-order impulsive ordinary and fractional differential equations with initial conditions

In this paper, using the idea of separated intervals in non-instantaneous impulsive equations, we initiate the study of initial value problems for mixed-order ordinary and fractional differential equations wit...

Authors: Suphawat Asawasamrit, Yasintorn Thadang, Sotiris K. Ntouyas and Jessada Tariboon

Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagation

In this paper, by taking two important network environment factors (namely point-to-group worm propagation and benign worms) into consideration, a mathematical model with multiple delays to model the worm prev...

Authors: Zizhen Zhang and Tao Zhao

Estimation for incomplete information stochastic systems from discrete observations

This paper is concerned with the estimation problem for incomplete information stochastic systems from discrete observations. The suboptimal estimation of the state is obtained by constructing the extended Kal...

Authors: Chao Wei

Analysis of coupled systems of implicit impulsive fractional differential equations involving Hadamard derivatives

We present some results on the existence, uniqueness and Hyers–Ulam stability to the solution of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional deriva...

Authors: Usman Riaz, Akbar Zada, Zeeshan Ali, Yujun Cui and Jiafa Xu

Effect of beam joinery on bridge structural stability

In this paper, we analyze the load deflection behavior of the superstructure elements of beam bridges under two different beam–beam connection designs. We present a mathematical model for beam–bridge structura...

Authors: Doungporn Wiwatanapataphee, Nathnarong Khajohnsaksumeth and Yong Hong Wu

Random attractors for Ginzburg–Landau equations driven by difference noise of a Wiener-like process

We consider a Wong–Zakai process, which is the difference of a Wiener-like process. We then prove that there are random attractors for non-autonomous Ginzburg–Landau equations driven by linear multiplicative n...

Authors: Fengling Wang, Jia Li and Yangrong Li

Cross soliton and breather soliton for the \((3+1)\)-dimensional Yu–Toda–Sasa–Fukuyama equation

Cross-soliton solution, breather soliton, periodic solitary solution, and doubly periodic solution are obtained by using an extended homoclinic test approach with perturbation parameter ...

Authors: Zhiqiang Pu and Zhigang Pan

Filter regularization method for a time-fractional inverse advection–dispersion problem

A filter regularization method is developed to solve a time-fractional inverse advection–dispersion problem, which is based on the modified ‘kernel’ idea. Proofs of convergence are given under both priori and ...

Authors: Songshu Liu and Lixin Feng

Certain generalized fractional calculus formulas and integral transforms involving \((p,q)\)-Mathieu-type series

In this paper, we establish sixteen interesting generalized fractional integral and derivative formulas including their composition formulas by using certain integral transforms involving generalized

Authors: Ravi P. Agarwal, Adem Kılıçman, Rakesh K. Parmar and Arjun K. Rathie

Impulsive fractional quantum Hahn difference boundary value problems

In this paper, we study the existence and uniqueness of solutions for two classes of boundary value problems for impulsive Caputo type fractional Hahn difference equations, by using the Banach contraction mapp...

Authors: Jessada Tariboon, Sotiris K. Ntouyas and Bundit Sutthasin

Exact traveling wave solutions of the space–time fractional complex Ginzburg–Landau equation and the space-time fractional Phi-4 equation using reliable methods

Ultrashort pulse propagation in optical transmission lines and phenomena in particle physics can be investigated via the cubic–quintic Ginzburg–Landau equation and the Phi-4 equation, respectively. The main ob...

Authors: Sekson Sirisubtawee, Sanoe Koonprasert, Surattana Sungnul and Takerngsak Leekparn

Analysis of advection-diffusion-reaction model for fish population movement with impulsive tagging: stability and traveling wave solution

So far, mobility in fish population has not been given sufficient attention, although movement and spatial heterogeneity can be an important dynamic feature that plays a critical role in their exploitation. Ha...

Authors: Chontita Rattanakul, Yongwimon Lenbury and Jeerawan Suksamran

The coupled method for singularly perturbed Volterra integro-differential equations

In this work a coupled (LDG-CFEM) method for singularly perturbed Volterra integro-differential equations with a smooth kernel is implemented. The existence and uniqueness of the coupled solution is given, pro...

Authors: Xia Tao and Yinghui Zhang

Invariant preserving schemes for double dispersion equations

We propose and study two finite difference schemes (FDSs) for the double dispersion equations. The first FDS is symplectic, while the second one preserves the discrete momentum exactly. Both FDS conserve the disc...

Authors: Natalia Kolkovska and Veselina Vucheva

Computation of iterative solutions along with stability analysis to a coupled system of fractional order differential equations

In this research article, we investigate sufficient results for the existence, uniqueness and stability analysis of iterative solutions to a coupled system of the nonlinear fractional differential equations (F...

Authors: Sajjad Ali, Thabet Abdeljawad, Kamal Shah, Fahd Jarad and Muhammad Arif

A numerical study of oil spill spreading in the Gulf of Thailand

An oil spill is the release of liquid petroleum into the marine ecosystem leading to huge damages in the natural resources. Prediction of oil spill spreading can help in handling accidental oil spills. This st...

Authors: Kittipong Srikhaetai, Kittisak Chayantrakom and Wattana Kanbua

Modified Saigo fractional integral operators involving multivariable H-function and general class of multivariable polynomials

In this paper, we establish modified Saigo fractional integral operators involving the product of a general class of multivariable polynomials and the multivariable H-function. The results established here are of...

Authors: D. L. Suthar, Belete Debalkie and Mitku Andualem

One dimensional fractional frequency Fourier transform by inverse difference operator

This article aims to develop fractional order convolution theory to bring forth innovative methods for generating fractional Fourier transforms by having recourse to solutions for fractional difference equatio...

Authors: Dumitru Baleanu, Maysaa Alqurashi, Meganathan Murugesan and Britto Antony Xavier Gnanaprakasam

An optimal consumption and investment problem with stochastic hyperbolic discounting

In this paper, we analyze the optimal consumption and investment problem of an agent by incorporating the stochastic hyperbolic preferences with constant relative risk aversion utility. Using the dynamic progr...

Authors: Yong Hyun Shin and Kum-Hwan Roh

Fractional optimal control in transmission dynamics of West Nile virus model with state and control time delay: a numerical approach

In this paper, an optimal control for a novel fractional West Nile virus model with time delay is presented. The proposed model is governed by a system of fractional delay differential equations, where the fra...

Authors: N. H. Sweilam, O. M. Saad and D. G. Mohamed

Stability analysis of a certain class of difference equations by using KAM theory

Authors: Senada Kalabušić, Emin Bešo, Naida Mujić and Esmir Pilav

A simple mathematical model for Guillain–Barré syndrome

In this paper, four different forms of a model to describe the dynamics of autoimmune diseases (with emphasis on Guillain–Barré syndrome) are proposed. In the first two cases, the immune response is supposed t...

Authors: Mohammed Fathy Elettreby, Elsayed Ahmed and Muntaser Safan

Analytical solution of the generalized Bagley–Torvik equation

Authors: Denghao Pang, Wei Jiang, Jun Du and Azmat Ullah Khan Niazi

Existence of positive solutions of discrete third-order three-point BVP with sign-changing Green’s function

Authors: Youji Xu, Weiwei Tian and Chenghua Gao

Stability analysis and traveling wave solution of a reaction–diffusion model for fish population incorporating time-dependent recruitment intensity

From the standpoint of fishery management, an essential component of the basic information upon which policy can be based consists of intelligence from field data and computations. In certain situations, these...

Authors: Jeerawan Suksamran and Yongwimon Lenbury

Reduction and normal forms for a delayed reaction–diffusion differential system with B–T singularity

In this paper, we expanded our computation to obtain a simpler and detailed reduction and normal form of a delayed reaction–diffusion differential system with Bogdanov–Takens (B–T) singularity. By using the ce...

Authors: Longyue Li, Jianzhi Cao and Yingying Mei

A one-dimensional mathematical simulation to salinity control in a river with a barrage dam using an unconditionally stable explicit finite difference method

Salinity refers to the amount of salt in rivers, where the salt can be in many different forms. There are two main methods of defining the concentration of salt in water such as the total dissolved solid measu...

Authors: Pornpon Othata and Nopparat Pochai

Extended r-central Bell polynopmials with umbral calculus viewpoint

Recently, extended r-central factorial numbers of the second kind and extended r-central Bell polynomials were introduced and various results of them were investigated. The purpose of this paper is to further der...

Authors: Lee-Chae Jang, Taekyun Kim, Dae San Kim and Han Young Kim

Mean-square heterogeneous synchronization of interdependent networks with stochastic disturbances

In this paper, the mean-square asymptotical heterogeneous synchronization of interdependent networks with stochastic disturbances, which is a zero-mean real Wiener process, is investigated. The network discuss...

Authors: Tianjiao Guo, Lilan Tu and Jiabo Chen

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

In recent years, many new definitions of fractional derivatives have been proposed and used to develop mathematical models for a wide variety of real-world systems containing memory, history, or nonlocal effec...

Authors: Elvin J. Moore, Sekson Sirisubtawee and Sanoe Koonprasert

Nonhomogeneous initial and boundary value problem for the Caputo-type fractional wave equation

In this paper, we give an analytical solution of a fractional wave equation for a vibrating string with Caputo time fractional derivatives. We obtain the exact solution in terms of three parameter Mittag-Leffl...

Authors: Mehmet Ali Özarslan and Cemaliye Kürt

Function matrix projective synchronization of non-dissipatively coupled heterogeneous systems with different-dimensional nodes

This paper regards function matrix projective synchronization of two different non-dissipatively coupled complex dynamical networks for different dimensions and different nodes. In this kind of complex dynamic...

Authors: Yanchao Shi, Xin Wang, Xiangyan Zeng and Yang Cao

Ternary-fractional differential transform schema: theory and application

In this article, we propose a novel fractional generalization of the three-dimensional differential transform method, namely the ternary-fractional differential transform method, that extends its applicability...

Authors: Feras Yousef, Marwan Alquran, Imad Jaradat, Shaher Momani and Dumitru Baleanu

Robust finite-time control of descriptor Markovian jump systems with impulsive

In this paper, we obtain sufficient conditions ensuring stability of the robust finite-time for descriptor Markovian jump systems with impulsive effects and time-varying norm-bounded disturbance, especially, w...

Authors: Xiaoming Su and Xiujie Zhao

The LS-SVM algorithms for boundary value problems of high-order ordinary differential equations

This paper introduces the improved LS-SVM algorithms for solving two-point and multi-point boundary value problems of high-order linear and nonlinear ordinary differential equations. To demonstrate the reliabi...

Authors: Yanfei Lu, Qingfei Yin, Hongyi Li, Hongli Sun, Yunlei Yang and Muzhou Hou

An application of forward difference method in robust stability of discrete uncertainty system with delays

This paper deals with the problems of robust stability for a class of uncertainty parameter systems with delays. By using a new Lyapunov–Krasovskii functional, quadratic inequality, and Schur complement techni...

Authors: Xianghui Zhou and Zizong Yan

On properties of solutions to Black–Scholes–Barenblatt equations

Authors: Xinpeng Li, Yiqing Lin and Weicheng Xu

Structure-preserving stochastic Runge–Kutta–Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noise

A class of stochastic Runge–Kutta–Nyström (SRKN) methods for the strong approximation of second-order stochastic differential equations (SDEs) are proposed. The conditions for strong convergence global order 1...

Authors: Qiang Ma, Yuanwei Song, Wei Xiao, Wendi Qin and Xiaohua Ding

Dynamical behaviors of a predator-prey system with prey impulsive diffusion and dispersal delay between two patches

In this paper, we consider a predator-prey model with prey impulsive diffusion and dispersal delay. By utilizing the dynamical properties of a single-species model with diffusion and dispersal delay between tw...

Authors: Haiyun Wan and Haining Jiang

Some identities of special numbers and polynomials arising from p-adic integrals on \(\mathbb{Z}_{p}\)

In recent years, studying degenerate versions of various special polynomials and numbers has attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Be...

Authors: Dae San Kim, Han Young Kim, Sung-Soo Pyo and Taekyun Kim

Existence of solutions for damped elastic systems in Banach spaces

In this article, we study the existence of mild solutions for damped elastic systems in Banach spaces. The discussion is based on the operator semigroup theory and fixed point theorem. In addition, two example...

Authors: Haide Gou and Yongxiang Li

Riemann–Hilbert approach and N-soliton solution for an eighth-order nonlinear Schrödinger equation in an optical fiber

This paper aims to present an application of the Riemann–Hilbert approach to treat higher-order nonlinear differential equation that is an eighth-order nonlinear Schrödinger equation arising in an optical fibe...

Authors: Zhou-Zheng Kang, Tie-Cheng Xia and Wen-Xiu Ma

Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays

This paper proposes a stochastic three species food-chain model with harvesting and distributed delays. Some criteria for the global dynamics of all positive solutions, including the existence of global positi...

Authors: Nafeisha Tuerxun, Zhidong Teng and Ahmadjan Muhammadhaji