Shugui Kang
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Shugui Kang has a total of 38 co-authors. Here are the top co-authors by number of shared publications:
Huiqin Chen
Shanxi Datong Univ, Sch Math & Stat, Xingyun St, Datong 037009, Peoples R China
8 shared publicationsJianmin Guo
Shanxi Datong Univ, Sch Math & Stat, Datong 037009, Peoples R China
5 shared publicationsYaqiong Cui
Shanxi Datong Univ, Sch Math & Stat, Xingyun St, Datong 037009, Peoples R China
4 shared publications- Huiqin Chen
School of Mathematics and Statistics, Shanxi Datong University, Datong, Shanxi 037009, China
3 shared publications - Lili Kong
The Institute of Applied Mathematics, Shanxi Datong University, Datong 037009, China
3 shared publications Caixia Guo
School of Mathematics and Computer Sciences, Shanxi Datong University, Shanxi, Datong 037009, China
2 shared publications
Latest Publications
- Open Access
- 3 October 2026
- Published by MDPI AG in Fractal and Fractional
- Vol. 10 (10) , 694
Solvability of a New Class of ψ-Fractional Unilateral Constrained Friction Problems
A new type of frictional contact problem is proposed in this paper. The nonlinear viscoelastic constitutive relationship we are considering contains -fractional differential terms. The contact conditions are controlled by fractional unilateral constraint conditions. The friction condition is given by a the generalized Clarke multivalued subdifferential function. Initially, by integrating Green’s theorem with findings from the multivalued operator theory, the problem is rephrased into a variational–hemivariational inequality framework. Subsequently, semi-discretization techniques are employed to establish the solvability of variational–hemivariational inequalities. Ultimately, these theoretical outcomes are transplanted to the friction contact model scenario, thus proving the existence of the latter’s solution.- 3 October 2026
- Published by MDPI AG in Fractal and Fractional
- Vol. 10 (10) , 694
Open AccessSolvability of a New Class of ψ-Fractional Unilateral Constrained Friction Problems
A new type of frictional contact problem is proposed in this paper. The nonlinear viscoelastic constitutive relationship we are considering contains -fractional differential terms. The contact conditions are controlled by fractional unilateral constraint conditions. The friction condition is given by a the generalized Clarke multivalued subdifferential function. Initially, by integrating Green’s theorem with findings from the multivalued operator theory, the problem is rephrased into a variational–hemivariational inequality framework. Subsequently, semi-discretization techniques are employed to establish the solvability of variational–hemivariational inequalities. Ultimately, these theoretical outcomes are transplanted to the friction contact model scenario, thus proving the existence of the latter’s solution. - 1 January 2026
- Published by Wilmington Scientific Publisher, LLC in Journal of Applied Analysis & Computation
- Vol. 16 (4) , 2019-2033
EXISTENCE AND MULTIPLICITY RESULTS FOR A CLASS OF DISCRETE FRACTIONAL PROBLEMS WITH SUMMATION BOUNDARY CONDITIONS
We study a discrete boundary value problem involving the Riemann-Liouville fractional operator. In particular, we introduce a discrete fractional summing boundary value problem that parallels the integral boundary value problem for fractional differential equations. By generalizing a commonly used fractional difference operator, we derive the corresponding Green's function and reformulate the problem as a fixed-point equation. The existence and multiplicity of positive solutions are established. Two illustrative examples are provided to demonstrate the applicability of the theoretical results, and numerical simulations are included for further validation.
- 1 January 2026
- Published by Wilmington Scientific Publisher, LLC in Journal of Applied Analysis & Computation
- Vol. 16 (4) , 2019-2033
EXISTENCE AND MULTIPLICITY RESULTS FOR A CLASS OF DISCRETE FRACTIONAL PROBLEMS WITH SUMMATION BOUNDARY CONDITIONS
We study a discrete boundary value problem involving the Riemann-Liouville fractional operator. In particular, we introduce a discrete fractional summing boundary value problem that parallels the integral boundary value problem for fractional differential equations. By generalizing a commonly used fractional difference operator, we derive the corresponding Green's function and reformulate the problem as a fixed-point equation. The existence and multiplicity of positive solutions are established. Two illustrative examples are provided to demonstrate the applicability of the theoretical results, and numerical simulations are included for further validation.
- 1 January 2024
- Published by Wilmington Scientific Publisher, LLC in Journal of Applied Analysis & Computation
- Vol. 14 (3) , 1771-1777
EXISTENCE OF OSCILLATORY SOLUTIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS
In this paper, we use Schauder-Tychonoff theorem to obtain a new sufficient condition for the global existence of oscillatory solutions for forced fractional delay differential equations.
- 1 January 2024
- Published by Wilmington Scientific Publisher, LLC in Journal of Applied Analysis & Computation
- Vol. 14 (3) , 1771-1777
EXISTENCE OF OSCILLATORY SOLUTIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS
In this paper, we use Schauder-Tychonoff theorem to obtain a new sufficient condition for the global existence of oscillatory solutions for forced fractional delay differential equations.
- 23 June 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 32, 164-169
Existence and Uniqueness of Positive Solutions for a Class of Fractional Differential Equation with Infinite-Point Boundary Value Conditions
The purpose of this paper is to discuss the existence and uniqueness of positive solutions for fractional differential equations with infinite-point boundary value conditions where $D_{0+}^{\alpha}$ is the standard Riemann-Liouville derivative of order $\alpha, \alpha > 2, n-1 < \alpha\leq n,j\in[1, n-2]$ is a fixed integer, $0 < \beta < \alpha-1, \eta_{j}\in R, 0 < \xi_{1} < \xi_{2} < \ldots < \xi_{j-1} < \xi_{j} <$ … $< 1(j=1,2,\ldots), \sum^{\infty}_{j=1}\eta_{j}\xi^{\alpha-\beta-1}_{j} \neq1$ . By means of fixed point theorems for mixed monotone operator with perturbation, some existence and uniqueness results of positive solutions are obtained.- 23 June 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 32, 164-169
Existence and Uniqueness of Positive Solutions for a Class of Fractional Differential Equation with Infinite-Point Boundary Value Conditions
The purpose of this paper is to discuss the existence and uniqueness of positive solutions for fractional differential equations with infinite-point boundary value conditions where $D_{0+}^{\alpha}$ is the standard Riemann-Liouville derivative of order $\alpha, \alpha > 2, n-1 < \alpha\leq n,j\in[1, n-2]$ is a fixed integer, $0 < \beta < \alpha-1, \eta_{j}\in R, 0 < \xi_{1} < \xi_{2} < \ldots < \xi_{j-1} < \xi_{j} <$ … $< 1(j=1,2,\ldots), \sum^{\infty}_{j=1}\eta_{j}\xi^{\alpha-\beta-1}_{j} \neq1$ . By means of fixed point theorems for mixed monotone operator with perturbation, some existence and uniqueness results of positive solutions are obtained.- 23 June 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 34, 158-163
Unique Nontrivial Solutions for a Class of Fractional Boundary Value Problem with Q-Derivatives
In this paper, we investigate unique nontrivial solution for a class nonlinear boundary value problem with fractional q-derivative where $D_{q}^{\alpha}$ are fractional q-derivative of Riemann-Liouville type, $b \geq 0, \beta \geq 0$ . Based on the fixed point theorems for increasing $\varphi-(h, e)$ -concave operators, we establish some sufficient conditions for the existence and uniqueness of nontrivial solution of the problem; on the other hand, an iterative scheme is constructed for approximating the nontrivial solution.- 23 June 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 34, 158-163
Unique Nontrivial Solutions for a Class of Fractional Boundary Value Problem with Q-Derivatives
In this paper, we investigate unique nontrivial solution for a class nonlinear boundary value problem with fractional q-derivative where $D_{q}^{\alpha}$ are fractional q-derivative of Riemann-Liouville type, $b \geq 0, \beta \geq 0$ . Based on the fixed point theorems for increasing $\varphi-(h, e)$ -concave operators, we establish some sufficient conditions for the existence and uniqueness of nontrivial solution of the problem; on the other hand, an iterative scheme is constructed for approximating the nontrivial solution.- 1 January 2023
- Published by Wilmington Scientific Publisher, LLC in Journal of Applied Analysis & Computation
- Vol. 13 (4) , 2074-2088
SMALLEST EIGENVALUES AND THE EXISTENCE RESULT FOR THE BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEMS
In this paper, we first discuss the existence of smallest eigenvalues of fractional boundary value problems. Then we consider the existence of at least one positive solution for a class of nonlinear boundary value problem of fractional differential system. Compared with the existing methods, our analysis relies on the fixed point index theorem in a Cartesian product of two cones. We further construct two special operators to compute straightforwardly the fixed point index in a suitable cone. Finally, we present an illustrative example to support our main result.
- 1 January 2023
- Published by Wilmington Scientific Publisher, LLC in Journal of Applied Analysis & Computation
- Vol. 13 (4) , 2074-2088
SMALLEST EIGENVALUES AND THE EXISTENCE RESULT FOR THE BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEMS
In this paper, we first discuss the existence of smallest eigenvalues of fractional boundary value problems. Then we consider the existence of at least one positive solution for a class of nonlinear boundary value problem of fractional differential system. Compared with the existing methods, our analysis relies on the fixed point index theorem in a Cartesian product of two cones. We further construct two special operators to compute straightforwardly the fixed point index in a suitable cone. Finally, we present an illustrative example to support our main result.
- Open Access
Reliability Evaluation and Optimization of a System with Mixed Run Shock
In this paper, we investigate a wear and mixed shock model in which the system can fail due to internal aging or external shocks. The lifetime of the system, due to internal wear, follows continuous phase-type (PH) distributions. The external random shocks arrive at the system according to a PH renewal process. The system will fail when the internal failure occurs or consecutive external shocks, the size of at least or consecutive external shocks the size of at least occur, where , . The failed system can be repaired immediately, and the repair times of the system are governed by continuous PH distributions. The system can be replaced by a new and identical one based on a bivariate replacement policy . The long-run average profit rate for the system is obtained by employing the closure property of the PH distribution. Finally, a numerical example is also given to determine the optimal replacement policy.Open AccessReliability Evaluation and Optimization of a System with Mixed Run Shock
In this paper, we investigate a wear and mixed shock model in which the system can fail due to internal aging or external shocks. The lifetime of the system, due to internal wear, follows continuous phase-type (PH) distributions. The external random shocks arrive at the system according to a PH renewal process. The system will fail when the internal failure occurs or consecutive external shocks, the size of at least or consecutive external shocks the size of at least occur, where , . The failed system can be repaired immediately, and the repair times of the system are governed by continuous PH distributions. The system can be replaced by a new and identical one based on a bivariate replacement policy . The long-run average profit rate for the system is obtained by employing the closure property of the PH distribution. Finally, a numerical example is also given to determine the optimal replacement policy. - Open Access
- 1 January 2022
- Published by Wiley in Discrete Dynamics in Nature and Society
- Vol. 2022 (1)
Dynamic Behavior of a Stochastic Tungiasis Model for Public Health Education
In this paper, we study the dynamic behavior of a stochastic tungiasis model for public health education. First, the existence and uniqueness of global positive solution of stochastic models are proved. Secondly, by constructing Lyapunov function and using It formula, sufficient conditions for disease extinction and persistence in the stochastic model are proved. Thirdly, under the condition of disease persistence, the existence and uniqueness of an ergodic stationary distribution of the model is obtained. Finally, the importance of public health education in preventing the spread of tungiasis is illustrated through the combination of theoretical results and numerical simulation.
- 1 January 2022
- Published by Wiley in Discrete Dynamics in Nature and Society
- Vol. 2022 (1)
Open AccessDynamic Behavior of a Stochastic Tungiasis Model for Public Health Education
In this paper, we study the dynamic behavior of a stochastic tungiasis model for public health education. First, the existence and uniqueness of global positive solution of stochastic models are proved. Secondly, by constructing Lyapunov function and using It formula, sufficient conditions for disease extinction and persistence in the stochastic model are proved. Thirdly, under the condition of disease persistence, the existence and uniqueness of an ergodic stationary distribution of the model is obtained. Finally, the importance of public health education in preventing the spread of tungiasis is illustrated through the combination of theoretical results and numerical simulation.
- Open Access
- 31 January 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (3) , 278
Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators
We study a class of nonlinear operators that can be written as the composition of a linear operator and a nonlinear map. We obtain results on fixed point index based on parameters that are related to the definitions of nonlinear spectra. As a particular case, existence of positive solutions for a second-order differential equation with separated boundary conditions is proved. The result also provides a spectral interval for the corresponding Hammerstein integral operator.
- 31 January 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (3) , 278
Open AccessNonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators
We study a class of nonlinear operators that can be written as the composition of a linear operator and a nonlinear map. We obtain results on fixed point index based on parameters that are related to the definitions of nonlinear spectra. As a particular case, existence of positive solutions for a second-order differential equation with separated boundary conditions is proved. The result also provides a spectral interval for the corresponding Hammerstein integral operator.
- Open Access
- 24 September 2020
- Published by Wiley in Discrete Dynamics in Nature and Society
- Vol. 2020, 1-6
On the Existence of Three Positive Solutions for a Caputo Fractional Difference Equation
In this paper, we introduce the application of three fixed point theorem by discussing the existence of three positive solutions for a class of Caputo fractional difference equation boundary value problem. We establish the condition of the existence of three positive solutions for this problem.
- 24 September 2020
- Published by Wiley in Discrete Dynamics in Nature and Society
- Vol. 2020, 1-6
Open AccessOn the Existence of Three Positive Solutions for a Caputo Fractional Difference Equation
In this paper, we introduce the application of three fixed point theorem by discussing the existence of three positive solutions for a class of Caputo fractional difference equation boundary value problem. We establish the condition of the existence of three positive solutions for this problem.