一类分数阶微分方程非分离边值问题的推广（英文）
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摘要
主要借助Banach不动点定理和Leray-Schauder度理论,考虑了一类分数阶微分方程非分离边值问题解的存在性和唯一性,并给出例子,推广了已有的结论.
In this paper,the existence and uniqueness results of the generalization nonlinear fractional differential equations with non-separated boundary conditions are investigated.The Banach's fixed point theorem and Leray-Schauder degree theory are applied to establish the results.Some examples are given to illustrate the main result.Relevant results are generalized and improved.
In this paper,the existence and uniqueness results of the generalization nonlinear fractional differential equations with non-separated boundary conditions are investigated.The Banach's fixed point theorem and Leray-Schauder degree theory are applied to establish the results.Some examples are given to illustrate the main result.Relevant results are generalized and improved.
引文
[1]PODLUBNY I.Fractional Differential Equations[M].San Diego:Academic Press,1999.
[2]KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and Applications of Fractional Differential Equations[M].Amsterdam:Elsevier,2006.
[3]BALEANU D,DIETHELM K,SCALAS E,et al.Fractional Calculus Models and Numerical Methods[M].Boston:World Scientific,2012.
[4]DEIMLING K.Nonlinear Functional Analysis[M].New York:Springer,1988.
[5]SAMKO S G,KILBAS A A,MARICHEV O L.Fractional Integrals and Derivatives:Theory and Applications[M].Yverdon:Gordon and Breach Science Publishers,1993.
[6]LAKSMIKANTHAM V,LEELA S,VASUNDHARA D J.Theory of Fractional Dynamics Systems[M].Cambridge:Cambridge Scientific Publishers,2009.
[7]AHMAD B,NIETO J J.Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory[J].Topological Methods in Nonlinear Analysis,2010,35(2):295-304.
[8]AHMAD B,NIETO J J.Anti-periodic fractional boundary value problems[J].Computers and Mathematics with Applications,2011,62(3):1150-1156.
[9]SABATIER J,AGRAWAL O P,MACHADO J A T.Advance in Fractional Calculus:Theoretical Developments and Applications in Physics and Engineering[M].Dordrecht:Springer,2007.
[10]DAFITARDAR-GEJJI V,BHALEKAR S.Boundary value problems for multi-term fractional differential equations[J].Journal of Mathematical Analysis and Applications,2008,345(2):754-765.
[11]ZHOU Y,PENG L.On the time-fractional Navier-Stokes equations[J].Computers and Mathematics with Applications,2017,73(6):874-891.
[12]BOULARES H,ARDJOUNI A,LASKRI Y.Existence and uniqueness of solutions for nonlinear fractional nabla difference systems with initial conditions[J].Fractional Differential Calculus,2017,7(2):247-263.
[13]ZHAO X H,CHAI C W,GE W G.Existence and nonexistence results for a class of fractional boundary value problems[J].Journal of Applied Mathematics and Computing,2013,41(1):17-31.
[14]FENG H X,ZHAI C B.Existence and uniqueness of positive solutions for a class of fractional differential equation with integral boundary conditions[J].Nonlinear Analysis:Modelling and Control,2017,22(2):160-172.
[15]SMART D R.Fixed Point Theorems[M].London:Cambridge University Press,1980.
[2]KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and Applications of Fractional Differential Equations[M].Amsterdam:Elsevier,2006.
[3]BALEANU D,DIETHELM K,SCALAS E,et al.Fractional Calculus Models and Numerical Methods[M].Boston:World Scientific,2012.
[4]DEIMLING K.Nonlinear Functional Analysis[M].New York:Springer,1988.
[5]SAMKO S G,KILBAS A A,MARICHEV O L.Fractional Integrals and Derivatives:Theory and Applications[M].Yverdon:Gordon and Breach Science Publishers,1993.
[6]LAKSMIKANTHAM V,LEELA S,VASUNDHARA D J.Theory of Fractional Dynamics Systems[M].Cambridge:Cambridge Scientific Publishers,2009.
[7]AHMAD B,NIETO J J.Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory[J].Topological Methods in Nonlinear Analysis,2010,35(2):295-304.
[8]AHMAD B,NIETO J J.Anti-periodic fractional boundary value problems[J].Computers and Mathematics with Applications,2011,62(3):1150-1156.
[9]SABATIER J,AGRAWAL O P,MACHADO J A T.Advance in Fractional Calculus:Theoretical Developments and Applications in Physics and Engineering[M].Dordrecht:Springer,2007.
[10]DAFITARDAR-GEJJI V,BHALEKAR S.Boundary value problems for multi-term fractional differential equations[J].Journal of Mathematical Analysis and Applications,2008,345(2):754-765.
[11]ZHOU Y,PENG L.On the time-fractional Navier-Stokes equations[J].Computers and Mathematics with Applications,2017,73(6):874-891.
[12]BOULARES H,ARDJOUNI A,LASKRI Y.Existence and uniqueness of solutions for nonlinear fractional nabla difference systems with initial conditions[J].Fractional Differential Calculus,2017,7(2):247-263.
[13]ZHAO X H,CHAI C W,GE W G.Existence and nonexistence results for a class of fractional boundary value problems[J].Journal of Applied Mathematics and Computing,2013,41(1):17-31.
[14]FENG H X,ZHAI C B.Existence and uniqueness of positive solutions for a class of fractional differential equation with integral boundary conditions[J].Nonlinear Analysis:Modelling and Control,2017,22(2):160-172.
[15]SMART D R.Fixed Point Theorems[M].London:Cambridge University Press,1980.