# Jinrong WangGuizhou University · Mathematics

Jinrong Wang

Ph.D

Fractional differential equations; Impulsive differential equations; Multi-agent Systems; Water wave equations;

## About

432

Publications

60,812

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10,308

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Citations since 2017

Introduction

Education

September 2006 - July 2009

## Publications

Publications (432)

In this paper, we investigate steady equatorial flows beneath solitary water waves subject to the Coriolis effect, which propagate over a flat bed. In particular, we focus on irrotational flows and present some properties of velocity field, behavior of the pressure and the extrema of the dynamic pressure. In addition, we provide some estimates for...

We introduce a non-instantaneous impulsive Hopfield neural network model in this paper. Firstly, we prove the existence and uniqueness of an almost periodic solution of this model. Secondly, we prove that the solution of this model is exponentially stable. Finally, we give an example of this model.

In this article, we study the impulsive consensus problem of linear multi-agent systems composed of-order conformable differential equations (∈ (0, 1]). Two cases of fixed and switching interaction networks are considered, respectively. Impulsive protocol of each agent is introduced based on the local information of the interaction networks. Firstl...

In this paper, we study the adaptive fixed-time consensus control for stochastic multi-agent systems (SMASs) with uncertain actuator faults. Firstly, a fully distributed adaptive consensus protocol and an adaptive fault-tolerant consensus protocol are proposed, respectively, to ensure that the fixed-time consensus of SMASs with actuator faults can...

This paper considers mean-square bounded consensus(MSBC) problems of double-integrator multi-agent systems(MASs) with both additive system noises and communication noises. It is shown that systems can achieve MSBC when multiple additive noises coexist. Applying algebra, graph theory and random analysis, several necessary and sufficient conditions f...

This article investigates the observability for Markovian jump Boolean network with random delay effect (MJBNRDE) in states which including two mutually independent Markov chains. First, the observability of MJBNRDE is converted into set reachability of the interconnected MJBNRDE by semi-tensor product and a parallel extension technique. Then, we d...

In this paper, we use Prandtl mixing-length theory and semiempirical theory to extend the classical problem of the wind in the steady atmospheric Ekman layer with constant eddy viscosity. New generalized atmospheric Ekman equations are established and qualitative properties of the corresponding ODEs are studied. Spatial wave solutions results for t...

We are committed to the study of neutral type differential equation with delay and pairwise permutable matrices on Yang’s fractal sets Rmκ(0<κ≤1,m∈N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemarg...

In this paper, we study the classical problem of the wind in the
steady atmospheric Ekman layer with constant eddy viscosity. The full nonlinear governing equations with the general boundary conditions are considered in the sense of modified β−plane approximation. Under the assumption of a flat surface and constant vorticity vector, we show that th...

This paper studies the controllability of the initial value problems of linear and semilinear second-order impulsive systems. Necessary and sufficient conditions of controllability for linear problems are obtained, and a new rank criterion is presented. We also show semilinear problems are controllable via Krasnoselskii's fixed point theorem. Final...

In this paper, solutions of fractional difference equations with Caputo-type delta-based fractional difference operator of order μ ∼ 1 are compared with solutions of corresponding limit difference equations with usual first-order forward difference. It is shown that the limit initial value problems differ substantially when μ → 1 − and μ → 1 +. To...

This paper investigates consensus control problem for a class of distributed parameter type multi-agent differential inclusion systems with state time-delay by utilizing iterative learning control (ILC). Unlike most ILC literature of nonlinear distributed parameter systems that require an identical virtual leader, the virtual leader is iteratively...

In this paper, we discuss the Hyers–Ulam stability of the linear recurrence over the
quaternion skew yield by considering the associated first-order matrix difference equations in complex Banach space. Firstly, we show the Hyers–Ulam stability result for the first-order quaternion-valued linear recurrence. Secondly, we give the sufficient
condition...

In this paper, periodic solutions of quaternion-valued impulsive differential equations
(QIDEs) are considered. First, the sufficient and necessary conditions to guarantee
periodic solutions are given for linear homogeneous QIDEs. Second, the representations of periodic solutions are derived by constructingGreen functions in one case, and the suffi...

In this paper, we investigate the motion of the wind in the steady atmospheric Ekman layer with suitable boundary conditions in ellipsoidal coordinates. Firstly, we consider the system with the piecewise eddy viscosity coefficients. When the eddy viscosity of the upper layer is constant and the eddy viscosity of the bottom layer is related to the h...

In this paper, we present the fundamental theory of linear quaternion-valued difference equations. Firstly, we derive general solutions for linear homogeneous equations and give the algorithm for calculating the fundamental matrix in the case of the diagonalizable form and Jordan form. Secondly, we apply the variation of the constant formula and Z...

In this paper, we introduce a modified delayed perturbation of discrete matrix exponential for impulsive linear discrete delay systems with non-permutable matrices. Using the Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgre...

In this paper, we investigate the averaging principle for Caputo-type fractional stochastic differential equations driven by Brownian motion. Different from the approach of integration by parts or decomposing integral interval to deal with the estimation of integral involving singular kernel in the existing literature, we show the desired averaging...

In this paper, we introduce a new kind of conformable stochastic impulsive differential systems (CSIDS) involving discrete distribution of Bernoulli. For random discontinuous trajectories, we modify the tracking error of piecewise continuous variables by a zero-order holder. First, the improved P -type and PD α -type learning laws of the random ite...

We develop a complex network-based SISqIqRS model, calculate the threshold R0 of infectious disease transmission and analyze the stability of the model. In the model, three control measures including isolation and vaccination are considered, where the isolation is structured in isolation of susceptible nodes and the isolation of infected nodes. We...

This paper deals with the spatially homogeneous Boltzmann equation for Fermi-Dirac particles for hard sphere model. Firstly, we prove the global existence and uniqueness of classical solutions to this problem and give the corresponding L∞ and L31 estimates of solutions. To achieve this aim, we give the global existence of an intermediate equation w...

In this paper, we study a new class of Sobolev type (ω, T)-periodic linear and semi-linear impulsive evolution equations, where T denotes a linear isomorphism from Banach space X to itself. We give a sufficient and necessary condition depending on the initial value, periodic boundary value and linear isomorphism to guarantee that the homogeneous li...

We study Hyers-Ulam stability for linear differential equations in the sense of quaternion-valued framework. This shows that Laplace transformation is also valid for finding the approximate solution for linear quaternion-valued differential equations.

In this paper, we firstly introduce the concept of conformable matrix sine and cosine functions, which help us to seek explicit formula of solutions to a conformable type linear oscillating system by using the variation of constants method. Secondly, we establish some sufficient conditions to guarantee the finite time stability results and give suf...

In this paper, we investigate the controllability of first-order impulsive fuzzy differential equations. Using the direct construction method, the controllability of first-order linear impulsive fuzzy differential equations is considered with a<0, the (c1) solution, and a<0, the (c2) solution, respectively.In addition, by employing the Banach fixed...

This article investigates the finite‐time consensus control for stochastic multi‐agent systems (SMASs) by using adaptive techniques. First, we propose a finite‐time adaptive consensus protocol for SMASs with node‐based adaptive law design method. Second, a finite‐time adaptive consensus protocol is also proposed for SMASs by adding a dynamical scal...

This paper studies (ω, c)-periodic solutions for time-varying non-instantaneous
impulsive differential equations. The Cauchy matrix of the time-varying
linear non-instantaneous impulsive system is constructed and some basic properties are derived. The method of constant variations and the adjoint matrix are used to find sufficient and necessary con...

In this paper, linear quaternion differential equations (LQDEs) with delay attracts our attention. In the light of delayed quaternion matrix exponential and the method of variation of constants, we derive the solutions of homogeneous and nonhomogeneous LQDEs with delay under the assumption of permutation matrices. Further, we investigate the soluti...

In this paper, we adopt a new approach to study the controllability and observability of linear quaternion-valued systems (QVS) from the point of complex-valued systems, which is much different from the method used in the previous paper. We show the equivalence relation of complete controllability for linear QVS and its complex-valued system. Then...

This paper investigates two non-instantaneous impulsive biological models. First, a non-instantaneous impulsive hematopoiesis model with pure delay and a non-instantaneous impulsive n-dimensional biological model with pure delay have been proposed. Next, the existence and uniqueness of almost periodic solutions for these two models are proved by us...

The resilient control problem of double-integrator stochastic multi-agent systems under denial-of-service (DoS) attack is studied in this paper. We neutralize the effects of DoS attacks by introducing a hidden layer that has no physical significance. Compared with previous works, this method requires less computation, does not require a high degree...

In this study, a quantized iterative learning control method with an encoding–decoding mechanism is investigated for networked control systems with constrained transmission bandwidths and random data dropouts at both the measurement and actuator sides. The intermittent update principle is used to address the problem of data asynchronism caused by t...

We study the geophysical fluid dynamical problem of the wind in the steady atmospheric Ekman layer with constant eddy viscosity. Three dimensional Ekman flows with constant vorticity is considered in the f −plane approximation. For non-equatorial f −plane approximation, we show that any bounded solution of the Ekman flow with a flat surface and con...

In this paper, we develop the Fourier transform approach to study the Hyers-Ulam stability of linear quaternion-valued differential equation with real coefficients and linear quaternion-valued even order differential equation with quaternion coefficients. It shows that Fourier transform is valid to find the approximate solutions for quaternion-valu...

In this work, with the aid of the representation of the solution, the relative controllability
for delaying linear discrete systems with a second-order difference is principally
investigated. Utilizing the delayed discrete matrix function, we give a sufficient criteria
for relative controllability, and construct a relevant control function. Lastly,...

In this paper, we study the irrational periodic equatorial surface travelling waves in flows without neglecting Coriolis forces due to the Earth's rotation. The monotonicity of horizontal velocity and pressure gradient distribution are obtained by the physical structures for the problem itself and the maximum principles.

In this paper, we firstly introduce a concept of conformable fractional delayed type matrix Cosine and Sine functions, which help us to construct an exact expression of a solution for the conformable fractional oscillating delay systems (CFODs). Secondly, we show existence and uniqueness of solutions of nonlinear conformable oscillating delay syste...

In this paper, we present a new general system of equations describing the steady motion of atmosphere with uniform density in ellipsoidal coordinates, which is derived from the general governing equations for viscous fluids. We first show that this new system can be reduced to the classic Ekman equations. Secondly, we obtain the explicit solution...

In this paper, based on the Euler equation and mass conservation equation in spherical coordinates, the ratio of the stratospheric average width to the planetary radius and the ratio of the vertical velocity to the horizontal velocity are selected as parameters under appropriate boundary conditions. We establish the approximate system using these t...

A new model that describes a dynamic frictional contact between a viscoelastic body and an obstacle is investigated in this paper. We consider a nonlinear viscoelastic constitutive law which involves a convex subdifferential inclusion term and thermal effects. The contact condition is modeled with unilateral constraint condition for a version of no...

In this paper, we are concerned with the incompressible and inviscid equatorial flows with discontinuous stratification. Firstly, arguing along the lines of Constantin and Johnson (J Phys Oceanogr 46:1935–1945, 2016), Henry and Martin (J Differ Equ 266:6788–6808, 2019, Dyn Partial Differ Equ 15:337–349, 2018, Arch Ration Mech Anal 233:497–512, 2019...

In this paper, we study a class of conformable frictionless contact problems with the surface traction driven by the conformable impulsive differential equation. The existence of a mild solution for conformable impulsive hemivariational inequality is obtained by the Rothe method, subjectivity of multivalued pseudomonotone operators and the property...

In this paper, we apply the strongly continuous cosine family of bounded linear operators to study the explicit representation of solutions for second order linear impulsive differential equations, and we give sufficient conditions for asymptotical stability of solutions. In addition we study the exponential stability of the linear perturbed proble...

We present an exact solution to the nonlinear governing equations in the β-plane approximation for geophysical edge waves at an arbitrary latitude. Such an exact solution is derived in the Lagrange framework, which describes trapped waves propagating eastward or westward along a sloping beach with a shoreline parallel to the latitude line. Using th...

In this paper, we introduce iterative learning control (ILC) schemes with varying trial lengths (VTL) to control impulsive multi-agent systems (I-MAS). We use domain alignment operator to characterize each tracking error to ensure that the error can completely update the control function during each iteration. Then we analyze the system’s uniform c...

This article considers the learning consensus problem of distributed parameter type multi‐agent differential inclusion systems including parabolic type and hyperbolic type. By imposing a Lipschitz condition on a set‐valued mapping and utilizing distributed P$$ P $$‐type iterative learning consensus control protocols, an iterative learning process i...

This paper gives a number of Ulam type stability results of first-order linear and first-order nonlinear impulsive fuzzy differential equations in different cases by applying an appropriate inequality and the direct analysis method. First, the Ulam type stability results of linear impulsive fuzzy differentiable equations under a<0, (c1)-differentia...

In this paper, we investigate the mean square consensus problem of leader-following nonlinear multiagent systems which suffer from white noise disturbance under randomly switching interaction topologies. The control protocol of each agent is designed based on its local information from its neighbors and the leader. Using matrix inequality theory an...

In this paper, we investigate the controllability of first order linear fuzzy differential systems. We use the direct construction method to derive the controllability results for three types of first order linear fuzzy controlled systems via (c1)-solution and (c2)-solution, respectively. An example is presented to illustrate our theoretical result...

This paper is involved with synchronization of fractional order stochastic systems in finite
dimensional space, and we have tested its time response and stochastic chaotic behaviors. Firstly, we give a representation of solution for a stochastic fractional order chaotic system. Secondly, some useful sufficient conditions are investigated by using m...

This paper uses the idea of fractional order accumulation instead of the form of grey index, and applies the fractional order accumulation prediction model to the economic growth prediction of the member states of the Group of Seven from 1973 to 2016. By comparing different evaluation indexes such as R2, MAD and BIC, it is found that the prediction...

In this paper, we study three-dimensional equatorial flows with constant vorticity beneath a wave train and above a flat bed in the modified β-plane approximation. It is proved that the equatorial flow is necessarily irrotational and the free surface is necessarily flat if it exhibits a constant vorticity, due to the incorporation of a gravitationa...

We investigate the exact solutions to the governing equations for the equatorial flows with the associated free surface and rigid bottom boundary conditions in the β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlen...

In this article, we study (ω, c)-periodic solutions for non-instantaneous impulsive systems and the time-varying coefficient A(t) is a family of unbounded linear operators. We show the existence and uniqueness of (ω, c)-periodic solutions using a fixed point theorem. An example is given to illustrate our results.

In this paper, we study the steady and purely azimuthal flow model representing the Antarctic Circumpolar Current, which is described as a semi-linear elliptic equation. By means of the Mercator projection, the mathematical model is transferred into a second order elliptic equation. We give sufficient conditions to guarantee the existence of soluti...

In this paper, we study three-dimensional equatorial flows with constant vorticity beneath a wave train and above a flat bed in the modified β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69...

In this paper, we study the existence of positive solutions for the nonlinear model of the Antarctic Circumpolar Current and analyze their Ulam-Hyers stability. By introducing some conditions on the ocean nonlinear vorticity function depending on other functions and initial values, we establish sufficient conditions to guarantee the existence, mult...

This paper studies conformable stochastic functional differential equations of neutral type. Firstly, the existence and uniqueness theorem of a solution is established. Secondly, the moment estimation and exponential stability results are given. Thirdly, the Ulam type stability in mean square is discussed. Finally, two examples are given to illustr...

This paper deals with the stability of linear quaternion-valued differential equations. First, we derive an explicit norm estimation like the matrix exponential function in the sense of quaternion-valued. Second, we use this norm to show that the first-order linear equations are asymptotically stable and Hyers-Ulam's type stable. Further, we show t...

This paper further investigates the classical problem of the wind in the steady atmospheric Ekman layer. For the case of eddy viscosity being subjected to a quadratic function, we construct an explicit solution, where the used approach is different from Delia [Analytical atmospheric Ekman-type solutions with height-dependent eddy viscosities. J Mat...

This paper further investigates the classical problem of the wind in the steady atmospheric Ekman layer. For the case of eddy viscosity being subjected to a quadratic function, we construct an explicit solution, where the used approach is different from Delia [Analytical atmospheric Ekman-type solutions with height-dependent eddy viscosities. J Mat...

This paper deals with the (ω,c)-periodic solutions to impulsive fractional differential equations with Caputo fractional derivative with a fixed lower limit. Firstly, a necessary and sufficient condition of the existence of (ω,c)-periodic solutions to linear problem is given. Secondly, the existence and uniqueness of (ω,c)-periodic solutions to sem...

In this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of g-expectation and give related properties of g-expectation. In addition, we find that the properties of conform...

The aim of this work is to investigate a mathematical model that describes the frictional contact between viscoelastic materials with a long memory and a moving foundation. The contact condition is modeled with a version of normal compliance condition with unilateral constraint in which wear of foundation is considered. Friction contact condition f...

This paper deals with iterative learning control for conformable impulsive differential equations. For nonlinear and linear problems varying with the initial state, we design standard P-type, Dγ -type, and conformable PIγDγ -type learning update laws. Next, we establish sufficient conditions for tracking error convergence and use impulsive
Gronwall...

In this paper, we study \begin{document}$ (\omega,\mathbb{T}) $\end{document}-periodic impulsive evolution equations via the operator semigroups theory in Banach spaces \begin{document}$ X $\end{document}, where \begin{document}$ \mathbb{T}: X\rightarrow X $\end{document} is a linear isomorphism. Existence and uniqueness of \begin{document}$ (\omeg...

In this manuscript, relative controllability of leader–follower multiagent systems with pairwise different delays in states and fixed interaction topology is considered. The interaction topology of the group of agents is modeled by a directed graph. The agents with unidirectional information flows are selected as leaders, and the others are followe...

In this paper, we study the standard problem of the wind in the steady atmospheric Ekman layer with classical boundary conditions. We consider the system with varying eddy viscosity coefficients that are small perturbation of a constant. We derive the explicit solution by using a different argument in the previous works. For two layers, the eddy vi...

In this chapter, we consider the ILC methods for the instantaneous impulsive system with deterministic, random and time-delay cases.

This chapter updates the controlled system of ILC from differential equation to differential inclusion. Sufficient conditions for convergence of ordinary differential inclusions and partial differential inclusions are given respectively.

This chapter introduces some related contents of fractional ILC.

This chapter introduces some related contents of fractional order multi-agent ILC. The design and convergence analysis of the controller are included, and some simulation examples are given.

This chapter summarizes the contents of this book and gives possible research directions in the future.

In this chapter, we study the ILC methods via fixed and varying trial lengths for the noninstantaneous impulsive system.

Iterative learning control (ILC) is an important branch of intelligent control, which
is applicable to robotics, process control and biological systems. ILC can be applied
not only to conventional fields but also to new systems such as fractional-order
systems, impulsive systems, delay systems and multi-agent systems raised from
physics, biology, p...

In this paper, relative controllability of impulsive multi-delay differential systems in finite dimensional space are studied. By introducing the impulsive multi-delay Gramian matrix, a necessary and sufficient condition, and the Gramian criteria, for the relative controllability of linear systems is given. Using Krasnoselskii’s fixed point theorem...

In this paper, we study fuzzy linear conformable differential equations using the generalized fuzzy conformable fractional differentiability concept. We give an explicit representation of q(1)- differentiable and q(2)-differentiable solutions for appropriate differential equations. Finally, we give some examples to illustrate our theoretical result...

In the framework of fixed topology and stochastic switching topologies, we study the mean-square bounded consensus(MSBC) of double-integrator stochastic multi-agent systems(SMASs) including additive system noises and communication noises. Combining algebra, graph theory and random analysis, we obtain several equivalent conditions for double-integra...

The networked structure has attracted significant attention due to high demand for industrial systems and rapid developments of network communication. Among various network randomness, fading is a common phenomenon, which can lead to signal attenuation, distortion, loss, and interference. This study concentrates on the point-to-point tracking probl...

In learning systems, high operation precision is often a desirable objective for the algorithm design. Though centralized algorithms are generally adopted, they are subjected to restrictive hypotheses on the learning systems. To overcome this challenging problem, we aim to propose some distributed learning algorithms that focus specifically on achi...

In this paper, we study the controllability and optimal control for a class of time-delayed fractional stochastic integro-differential system with Poisson jumps. A set of sufficient conditions is established for complete and approximate controllability by assuming non-Lipschitz conditions and pth mean square norm. We also give an existence of optim...

We study a new frictionless quasistatic contact problem for viscoelastic materials, in which contact conditions are described by the fractional Clarke generalized gradient of nonconvex and nonsmooth functions and a time-delay system. In addition, our constitutive relation is modeled using the fractional Kelvin–Voigt law with long memory. The existe...

In this paper, we consider the continuous dependence and differentiability of solutions of second-order impulsive differential equations on initial values and impulsive points. By constructing a sequence of iterations, we show the existence of solutions with the perturbation of initial values and impulsive points and the continuous dependence of so...

In this paper, we study the relative controllability of a fractional stochastic system with pure delay in finite dimensional stochastic spaces. A set of sufficient conditions is obtained for relative exact controllability using fixed point theory, fractional calculus (including fractional delayed linear operators and Grammian matrices) and local as...