Boundary value problem for a coupled system of fractional differential equations with p-Laplacian operator at resonance
CHENG Ling-ling1, LIU Wen-bin1, YE Qing-qing2
1. College of Science, China University of Mining and Technology, Xuzhou Jiangsu 221116, China;
2. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
CHENG Ling-ling, LIU Wen-bin, YE Qing-qing. Boundary value problem for a coupled system of fractional differential equations with p-Laplacian operator at resonance[J]. Journal of East China Normal University(Natural Sc, 2014, 2014(3): 30-39.
{1} HEGAZI A S, AHMED E, MATOUK A E. On chaos control and synchronization of the commensurate fractional order Liu system [J]. Communications in Nonlinear Science \& Numerical Simulation, 2013, 18: 1193-1202.{2} SANDERSE B. Energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations [J]. Journal of Computational Physics, 2013, 233: 100-131.{3} KILBAS A A. Theory and Applications of Fractional Differential Equations [M]. Amsterdam: Elsevier Science, 2006.{4} MILLER K S. An Introduction to the Fractional Calculus and Differential Equations [M]. New York: John \& Wiley, 1993.{5} LAKSHMIKANTHAM V, VATSALA A S. Basic theory of fractional differential equations [J]. Nonlinear Analysis: Theory, Methods \& Applications, 2008, 69: 2677-2682.{6} BABAKHANI A, DAFTARDAR G V. Existence of positive solutions for N-term non-autonomous fractional differential equations [J]. Positivity, 2005, 9: 193-206.{7} BAI C Z. Positive solutions for nonlinear fractional differential equations with coefficient that changes sign [J]. Nonlinear Analysis: Theory, Methods \& Applications, 2006, 64: 677-689.{8} AGARWAI R P, OREGA D, STANEK S. Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations [J]. Journal of Mathematical Analysis and Applications , 2008, 69: 2677-2682.{9} BENCHOHRA M, HENDERSON J, NTOUYAS SK. Existence results for positive solutions for fractional order functional differential equations with infinite delay [J]. Journal of Mathematical Analysis and Applications, 2005, 338: 1340-1350.{10} ZHOU W, PENG J. Existence of solutions to boundary value problem for fractional differential equations [J]. Chinese Journal of engineering Mathematics, 2011, 28: 727-735.{11} AHMADB, SIVASUNDARAM S. Existence results for nonlinear impulsive hybrid boundary value problem involving fractional differential equations [J]. Nonlinear Analysis: Hybrid Systems, 2009, 3: 251-258.{12} BAI Z, LV H. Positive solutions for boundary value problem of nonlinear fractional differential equation [J]. Journal of Mathematical Analysis and Applications, 2005, 311: 495-505.{13} WANG G, LIU W, ZHU S. The existence solutions for a fractional 2m-point boundary value problems [J]. Journal of Applied Mathematics, 2012: 2012: 1-14.{14} ZHANG Y, BAI Z. Existence of solutions for nonlinear fractional three-point boundary value problems at resonance [J]. Journal of Applied Mathematics and Computing, 2012, 36: 417-440.{15} ZHANG s, ZHANG J. Positive solutions for boundary-value problems of nonlinear fractional differential equation [J]. Nonlinear Analysis: Theory, Methods \& Applications, 2006, 36: 1-12.{16} LIANG s, LV H. Positive solutions for boundary value problem of nonlinear fractional differential equation [J]. Journal of Mathematical Analysis and Applications, 2009, 71: 5545-5550.{17} BENCHOHRA M, HAMANI S, NTOUYAS SK. Boundary value problem for differential equations with fractional order and nonlocal conditions [J]. Nonlinear Analysis: Theory, Methods \& Applications, 2009, 71: 2391-2396.{18} CHEN T, LIU W, CHENG Y. Antiperiodic solutions for Linard-type differential equation with p-Laplacian operator [J]. Boundary Value Problems, 2010, 2010: 1-12.{19} LIAN L, GE W. The existence of solutions of m-point \emph{p}-Laplacian boundary value problems at resonance [J]. Acta Mathematicae Applicatae Sinica, 2005, 28: 288-295.{20} LIU B. On the existence of solutions for the periodic boundary value problems with \emph{p}-Laplacian operator [J]. Jouranl of systems Science Mathematical Sciences, 2003, 23: 76-85.{21} FENG H, A symmetric solution of a multipoint boundary value problem with one-dimensional p-Laplacian at resonance [J]. Nonlinear Analysis: Theory, Methods \& Applications, 2008, 10: 3964-3972.{22} SU X. Boundary value problem for a coupled system of nonlinear fractional differential equations [J]. Applied Mathematics Letters, 2009, 22: 64-69.{23} JIANG W. Solvability for a coupled system of fractional differential equations at resonance [J]. Nonlinear Analysis: Real World Applications, 2012, 13: 2285-2292.{24} GE W, REN. An extension of Mawhin's continuation theorem and its application to boundary value problems with p-Laplacian . Nonlinear Analysis, 2004, 58: 477-488.{25} PODLUBNY I. Fractional differential equation [M]. San Diego: Academic Press, 1999.{26} SAMKO S G. Fractional integrals and derivatives: Theory and Applications [M]. Switzerland: Gordon and Breach, 1993.{27} LAKSHMIKANTHAM V. Theory of fractional dynamic systems [M]. Cambridge: Cambridge Academic Publishers, 2009.
中国综合性科技类核心期刊(北大核心)