段俊生

  教授 硕士生导师
上海应用技术大学 理学院

电话: (86-021-60877330)
传真: (86-021-60873193)
E-mail: duanjs@sit.edu.cn

主页：http://blog.sciencenet.cn/u/duanjs

教  育

博士，应用数学，山东大学，济南，中国（1999,9-2002,6）

硕士，应用数学，内蒙古大学，呼和浩特，中国（1993,9-1996,6）

学士，数学，内蒙古大学，呼和浩特，中国（1982,9-1986,6）

工作经历

 2016.10 – 至今：上海应用技术大学理学院

 2015.10 – 2016.09：加州大学默塞德分校高级访问学者

 2009.05 – 2015.09：上海应用技术大学理学院

 2002.08 – 2009.04：天津商业大学理学院

 1986.07 - 1999.08：内蒙古工业大学理学院

教学

数学分析，微分方程，高等代数，复变函数，空间解析几何，高等数学，线性代数，数学文化，数值分析，等。 所授课程《数学分析1》获2013年上海应用技术大学“我喜爱的课程”奖。

研究兴趣

非线性分析,分数阶微积分，非线性微分方程，分数阶微分方程，粘弹性力学建模与分析，动力系统，模糊代数,等。

研究项目

主持在研国家自然科学基金项目和上海自然科学基金项目各1项。

主持完成天津市教委和上海市教委科研项目各1项；主持完成上海自然科学基金项目1项；作为主要成员参加完成国家自然科学基金项目3项。

论文

发表科研论文120余篇，其中SCI检索60余篇。论文代表作:

[74]Junsheng Duan, Lian Chen, Solution of fractional differential equation systems and computation of matrix Mittag–Leffler functions, Symmetry, 2018, Vol.10 (No.10), 503 (14 pages).

 [73]Jun-Sheng Duan, Dumitru Baleanu, Steady periodic response for a vibration system with distributed order derivatives to periodic excitation, Journal of Vibration and Control, 2018, Vol. 24, issue 14, 3124-3131.  

[72]Junsheng Duan, A generalization of the Mittag–Leffler function and solution of system of fractional differential equations, Advances in Difference Equations, (2018) 2018:239 (12 pages).  

[71]Jun-Sheng Duan, Xiang Qiu, Stokes’ second problem of viscoelastic fluids with constitutive equation of distributed-order derivative, Applied Mathematics and Computation 331 (2018) 130-139.  

 [70]Jun-Sheng Duan, The boundary value problems for fractional ordinary differential equations with Robin boundary conditions, Int. J. Appl. Math. Stat. Vol. 57, No. 2, 2018; 200-214.

[69]Lingjie Duan, Junsheng Duan*, A generalized constitutive equation with distributed order derivative for viscoelastic solid, International Journal of Materials, Mechanics and Manufacturing, Vol. 6, No. 3, 2018, 191-194. (*Corresponding author)

[68]Jun-Sheng Duan, Lei Lu, Lian Chen, Yu-Lian An, Fractional model and solution for the Black-Scholes equation, Math Meth Appl Sci. 2018, Volume 41, Issue 2, Pages 697-704.  

 [67]Jun-Sheng Duan, Cui-Ping Cheng, Lian Chen, A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives, Open Phys. 2017, Volume 15, Issue 1, 809–818.

[66]Jun-Sheng Duan, YangQuan Chen, Mechanical response and simulation for constitutive equations with distributed order derivatives, Int. J. Model. Simul. Sci. Comput. 2017, Volume 8, Issue 4, 1750040 (16 pages).

 [65]Jun-Sheng Duan, Randolph Rach, Abdul-Majid Wazwaz, Higher order numeric solutions of the Lane-Emden-type equations derived from the multi-stage modified Adomian decomposition method, International Journal of Computer Mathematics, 2017, Vol. 94, Issue 1, 197-215.

[64]Junsheng Duan, Zongxue Li, Jinyuan Liu, Pull-in instability analyses for NEMS actuators with quartic shape approximation, Applied Mathematics and Mechanics, Volume 37, Issue 3, pp 303-314, 2016.   

[63]C. Huang and J.-S. Duan*, Steady-state response to periodic excitation in fractional vibration system, Journal of Mechanics, 2016, volume 32, issue 01, pp. 25-33. (*Corresponding author)

[62]Jun-Sheng Duan, A modified fractional derivative and its application to fractional vibration equation, Applied Mathematics & Information Sciences (Appl. Math. Inf. Sci.) Vol.10, No. 5, 1863-1869 (2016). doi:10.18576/amis/100527

[61]Jun-Sheng Duan, Temuer Chaolu, Zhong Wang, Shou-Zhong Fu, Lévy stable distribution and space-fractional Fokker-Planck type equation, Journal of King Saud University - Science，Volume 28, Issue 1, January 2016, Pages 17–20.  

[60]L. Bougoffa, J.-S. Duan, R.C. Rach, Exact and approximate analytic solutions of the thin film flow of fourth-grade fluids by the modified Adomian decomposition method, International Journal of Numerical Methods for Heat and Fluid Flow,Vol. 26, No. 8, 2016, pp. 2432-2440.  

[59]Randolph Rach, Jun-Sheng Duan, Abdul-Majid Wazwaz, Solution of higher-order, multipoint, nonlinear boundary value problems with high-order Robin-type boundary conditions by the Adomian decomposition method, Appl. Math. Inf. Sci. Vol.10, No. 4, 1231-1242 (2016).

[58]Randolph Rach, Jun-Sheng Duan, and Abdul-Majid Wazwaz, Solving the two-dimensional Lane-Emden type equations by the Adomian decomposition method, Journal of Applied Mathematics and Statistics (2016) Vol. 3 No. 1 pp. 15-26.  

[57]Abdul-Majid Wazwaz, Randolph Rach, Jun-Sheng Duan, Variational iteration method for solving oxygen and carbon substrate concentrations in microbial floc particles, MATCH Commun. Math. Comput. Chem. 76, No.2, (2016) 511-523.  

[56]Amin Farrokhabadia, Abed Mohebshahedin, Randolph Rach, Jun-Sheng Duan, An improved model for the cantilever NEMS actuator including the surface energy, fringing field and Casimir effects, Physica E: Low-dimensional Systems and Nanostructures, 2016, 75, 202-209.

 [55]Jun-Sheng Duan, Randolph Rach, Abdul-Majid Wazwaz, Oxygen and carbon substrate concentrations in microbial floc particles by the Adomian decomposition method, MATCH-Commun. Math. Comput. Chem. Volume 73 (2015) number 3，pp. 785-796.

[54]Jun-Sheng Duan, Randolph Rach, Abdul-Majid Wazwaz, Steady-state concentrations of carbon dioxide absorbed into phenyl glycidyl ether solutions by the Adomian decomposition method, Journal of Mathematical Chemistry, Volume 53, Issue 4 (2015), 1054-1067.

[53]Jun-Sheng Duan, Can Huang, Li-Li Liu, Response of a fractional nonlinear system to harmonic excitation by the averaging method, Open Physics, vol.13, No.1, 177-182, 2015.

[52]Li-Li Liu, Jun-Sheng Duan*, A detailed analysis for the fundamental solution of fractional vibration equation, Open Mathematics, 2015, Volume 13, Issue 1, 826-838. (*Corresponding author)

[51]Jun-Sheng Duan, Randolph Rach, Abdul-Majid Wazwaz, A reliable algorithm for positive solutions of nonlinear boundary value problems by the multistage Adomian decomposition method, Open Engineering, Volume 5, Issue 1, 59-74, 2015.  

[50]Lei Lu, Junsheng Duan*, Longzhen Fan, Solution of the magnetohydrodynamics Jeffery-Hamel flow equations by the modified Adomian decomposition method, Adv. Appl. Math. Mech., 2015, Vol. 7, No. 5, pp. 675-686. (*Corresponding author)

[49]Randolph Rach, Jun-Sheng Duan*, Abdul-Majid Wazwaz, On the Solution of Non-Isothermal Reaction-Diffusion Model Equations in a Spherical Catalyst by the Modified Adomian Method, Chemical Engineering Communications, Vol.202, Issue 8, 2015, 1081-1088. (*Corresponding author)

 [48]Abdul-Majid Wazwaz, Randolph Rach, Jun-Sheng Duan*, Solving New Fourth-order Emden-Fowler-Type Equations by the Adomian Decomposition Method, International Journal for Computational Methods in Engineering Science and Mechanics, 16 (2) (2015), 121-131. (*Corresponding author)  

[47]Randolph Rach, Abdul-Majid Wazwaz, Jun-Sheng Duan*, The Volterra integral form of the Lane-Emden equation: New derivations and solution by the Adomian decomposition method, J. Appl. Math. Comput. Volume 47, Issue 1 (2015), 365-379. (*Corresponding author)

 [46]Lian Chen, Junsheng Duan*, Multistage Numerical Picard Iteration Methods for Nonlinear Volterra Integral Equations of the Second Kind. Advances in Pure Mathematics, (2015) 5, 672-682. (*Corresponding author)

[45]Jun-Sheng Duan, Randolph Rach, The Degenerate Form of the Adomian Polynomials in the Power Series Method for Nonlinear Ordinary Differential Equations, Journal of Mathematics and System Science, Volume 5, Number 10, (2015) 411-428.

[44]Jun-Sheng Duan, The Adomian polynomials and the new modified decomposition method for BVPs of nonlinear ODEs, Mathematical Computation, Volume 4, Issue 1, 2015,1-6.

[43]Lazhar Bougoffa, Randolph Rach, Abdul-Majid Wazwaz, Jun-Sheng Duan, On the Adomian decomposition method for solving the Stefan problem, International Journal of Numerical Methods for Heat & Fluid Flow，Vol. 25, No. 4, 2015, pp. 912-928.

[42]Zhong Wang, Shou-Zhong Fu, Jun-Sheng Duan, Expansion of eigenfunctions of regular J-self-adjoint differential operators, Pacific Journal of Applied Mathematics, 6(3), pp 1-16, 2014.

[41]Lei Lu, Jun-Sheng Duan, Long-Zhen Fan, Solution of two-dimensional viscous flow in a rectangular domain by the modified decomposition method, CMES-Comput. Model. Eng. Sci. Vol. 100, No. 6, pp. 463-475, 2014.

[40]A.-M. Wazwaz, R. Rach, L. Bougoffa, J.-S. Duan, Solving the Lane–Emden–Fowler type equations of higher orders by the Adomian decomposition method, CMES: Computer Modeling in Engineering & Sciences, Vol. 100, No. 6, pp. 507-529, 2014.

[39]Yin-shan Yun, Temuer Chaolu, Jun-sheng Duan, A segmented and weighted Adomian decomposition algorithm for boundary value problem of nonlinear groundwater equation, Math. Meth. Appl. Sci. 2014, 37, 2406–2418.

[38]Lei Lu, Jun-Sheng Duan*, How to select the value of the convergence parameter in the Adomian decomposition method, CMES: Computer Modeling in Engineering & Sciences, Vol. 97, No. 1, pp. 35-52, 2014. (*Corresponding author)

[37]Randolph Rach, Abdul-Majid Wazwaz, Jun-Sheng Duan*, A reliable analysis of oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, International Journal of Biomathematics, Vol. 7, No. 2 (2014) 1450020 (12 pages). (*Corresponding author)

[36]Jun-Sheng Duan, Ai-Ping Guo, and Wen-Zai Yun, Similarity Solution for Fractional Diffusion Equation, Abstract and Applied Analysis, Volume 2014 (2014), Article ID 548126, 5 pages.

[35]Jun-Sheng Duan, Xiang Qiu, The periodic solution of Stokes' second problem for viscoelastic fluids as characterized by a fractional constitutive equation, Journal of Non-Newtonian Fluid Mechanics, 205 (2014) 11-15.

[34]Jun-Sheng Duan, Zhong Wang, Shou-Zhong Fu, The zeros of the solutions of the fractional oscillation equation, Fract. Calc. Appl. Anal. Vol. 17, No 1 (2014), pp. 10-22.

[33]Jun-Sheng Duan, Shou-Zhong Fu, Zhong Wang, Fractional diffusion-wave equations on finite interval by Laplace transform, Integral Transforms and Special Functions, 2014, Vol.25, No. 3, 220-229.

[32]Abdul-Majid Wazwaz, Randolph Rach, Jun-Sheng Duan, A study on the systems of the Volterra integral forms of the Lane–Emden equations by the Adomian decomposition method, Math. Meth. Appl. Sci., 2014, Vol.37, Issue 1, 10-19.

[31]Randolph Rach, Jun-Sheng Duan*, Abdul-Majid Wazwaz, Solving coupled Lane-Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method, J. Math. Chem. 2014, Vol.52, Issue 1, 255-267. (*Corresponding author)

[30]Abdul-Majid Wazwaz, Randolph Rach and Jun-Sheng Duan, The modified Adomian decomposition method and the noise terms phenomenon for solving nonlinear weakly-singular Volterra and Fredholm integral equations, Central European Journal of Engineering, Volume 3, Issue 4, 2013, Pages 669-678.

[29]Shou-Zhong Fu, Zhong Wang and Jun-Sheng Duan*, Solution of quadratic integral equations by the Adomian decomposition method, CMES-Comput. Model. Eng. Sci. Vol. 92, No. 4, pp. 369-385, 2013. (*Corresponding author)

[28]Jun-Sheng Duan, Randolph Rach, A pull-in parameter analysis for the cantilever NEMS actuator model including surface energy, fringing field and Casimir effects, International Journal of Solids and Structures, 50 (2013) 3511-3518.  

[27]Jun-Sheng Duan, Zhong Wang, Shou-Zhong Fu, Fractional diffusion equation in half-space with Robin boundary condition, Central European Journal of Physics, 2013, Vol.11, Issue 6, 799-805.  

[26]Jun-Sheng Duan, Randolph Rach, Abdul-Majid Wazwaz, Temuer Chaolu, Zhong Wang, A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions, Applied Mathematical Modelling 37 (2013), pp. 8687-8708.  

[25]Jun-Sheng Duan, Randolph Rach and Abdul-Majid Wazwaz, A new modified Adomian decomposition method for higher-order nonlinear dynamical systems, CMES-Comput. Model. Eng. Sci., Vol. 94, No. 1, pp. 77-118, 2013.  

[24]Jun-Sheng Duan, The periodic solution of fractional oscillation equation with periodic input, Advances in Mathematical Physics, Volume 2013 (2013), Article ID 869484, 6 pages.

[23]Jun-Sheng Duan, Temuer Chaolu, Randolph Rach, Lei Lu, The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations, Computers and Mathematics with Applications, 2013,Volume 66, Issue 5, Pages 728-736.

[22]Jun-Sheng Duan, Zhong Wang, Shou-Zhong Fu, Temuer Chaolu, Parametrized temperature distribution and efficiency of convective straight fins with temperature-dependent thermal conductivity by a new modified decomposition method, International Journal of Heat and Mass Transfer, Vol. 59 (2013) 137-143.

[21]Jun-Sheng Duan, Randolph Rach, Shi-Ming Lin, Analytic approximation of the blow-up time for nonlinear differential equations by the ADM-Pade technique, Math. Meth. Appl. Sci. 36 (13) (2013) 1790-1804.  

[20]Jun-Sheng Duan, Zhong Wang, Yu-Lu Liu, Xiang Qiu, Eigenvalue problems for fractional ordinary differential equations, Chaos, Solitons & Fractals, Vol 46 (2013) 46-53.  

[19]Jun-Sheng Duan, Randolph Rach, Abdul-Majid Wazwaz, Solution of the model of beam-type micro- and nano-scale electrostatic actuators by a new modified Adomian decomposition method for nonlinear boundary value problems, International Journal of Non-Linear Mechanics, Vol. 49 (2013) 159-169.  

[18]Xiang Qiu, Junsheng Duan, Jianping Luo, Purna N. Kaloni, Yulu Liu, Parameter effects on shear stress of Johnson–Segalman fluid in Poiseuille flow, International Journal of Non-Linear Mechanics, 55 (2013) 140-146.  

[17]Randolph Rach, Abdul-Majid Wazwaz, Jun-Sheng Duan*, A reliable modification of the Adomian decomposition method for higher-order nonlinear differential equations, Kybernetes, Vol. 42, No. 2 (2013) 282-308. (*Corresponding author)  

[16]Abdul-Majid Wazwaz, Randolph Rach, Jun-Sheng Duan, Adomian decomposition method for solving the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions, Applied Mathematics and Computation, Vol. 219, Issue 10 (2013) 5004-5019.  

[15]Jun-Sheng Duan, Temuer Chaolu, Randolph Rach, Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach-Adomian-Meyers modified decomposition method, Applied Mathematics and Computation, Vol. 218, Issue 17 (2012) 8370-8392.  

[14]Jun-Sheng Duan, Randolph Rach, Higher-order numeric Wazwaz-El-Sayed modified Adomian decomposition algorithms, Computers & Mathematics with Applications, Vol. 63, Issue 11 (2012)  Pages 1557-1568.  

[13]Jun-Sheng Duan, Randolph Rach, A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations, Applied Mathematics and Computation, Vol. 218, Issue 8 (2011) 4090-4118.  

[12]Jun-Sheng Duan, Randolph Rach, New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods,  Applied Mathematics and Computation, Vol. 218, Issue 6 (2011) 2810-2828.  

[11]Jun-Sheng Duan, New ideas for decomposing nonlinearities in differential equations, Applied Mathematics and Computation, Vol. 218, Issue 5 (2011) 1774-1784.  

[10]Jun-Sheng Duan, New recurrence algorithms for the nonclassic Adomian polynomials, Computers & Mathematics with Applications, Vol. 62, Issue 8 (2011) 2961-2977.  

[9]Jun-Sheng Duan, Ai-Ping Guo, Fen-Xia Zhao, Li Xu, Wen-Guang Tang, Standard bases of a vector space over a linearly ordered incline, Communications in Algebra, Vol. 39, No. 4 (2011) 1404-1412.  

[8]Jun-Sheng Duan, Convenient analytic recurrence algorithms for the Adomian polynomials, Applied Mathematics and Computation, Vol. 217, Issue 13 (2011) 6337-6348.  

[7]Randolph Rach, Jun-Sheng Duan*, Near-field and far-field approximations by the Adomian and asymptotic decomposition methods, Applied Mathematics and Computation, Vol. 217, Issue 12 (2011) 5910-5922.（*Corresponding author）

[6]Jun-Sheng Duan, An efficient algorithm for the multivariable Adomian polynomials,  Applied Mathematics and Computation, Vol. 217, Issue 6 (2010) 2456-2467.  

[5]Jun-Sheng Duan, Recurrence triangle for Adomian polynomials, Applied Mathematics and Computation, Vol. 216, Issue 4 (2010) 1235-1241.  

 [4]Jun-Sheng Duan, Ai-Ping Guo, Reduced polynomials and their generation in Adomian decomposition methods, CMES-Comput. Model. Eng. Sci., Vol. 60, No. 2 (2010) 139-150.  

[3]Jun-Sheng Duan, Time- and space-fractional partial differential equations, Journal of Mathematical Physics, 2005, Vol. 46, No. 1: 13504-13511.

[2]Jun-Sheng Duan, The transitive closure, convergence of powers and adjoint of generalized fuzzy matrices, Fuzzy Sets and Systems, 2004, Vol. 145, No. 2: 301-311.  

[1]DUAN Jun-sheng, XU Ming-yu, Concentration distribution of fractional anomalous diffusion caused by an instantaneous point source, Applied Mathematics and Mechanics, 2003, Vol. 24, No. 11: 1302-1308.