广义凹算子定理在分数阶脉冲边值问题中的研究
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摘要
运用广义凹算子的不动点定理,研究了一类分数阶脉冲边值问题,得到了存在唯一解的新判据.最后,给出一个例子说明结论的可行性.
By using a fixed point theorem for a generalized concave operator, a new criterion for the existence and uniqueness of solutions involving a fractional order and impulsive boundary conditions is established. Finally, an example is given to illustrate the main results.
By using a fixed point theorem for a generalized concave operator, a new criterion for the existence and uniqueness of solutions involving a fractional order and impulsive boundary conditions is established. Finally, an example is given to illustrate the main results.
引文
[1] ZHANG L,ZHAI C.Existence and uniqueness of positive solutions to nonlinear second order impulsive differential equations with concave or convex nonlinearities[J].Discrete Dynamics in Nature and Society,2013,2013(1):165-177.
[2] ZHAO K,GONG P.Positive solutions for impulsive fractional differential equations with generalizedperiodic boundary value conditions[J].Advances in Difference Equations,2014,2014(1):255.
[3] AHMAD B,SIVASUNDARAM S.Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations[J].Nonlinear Analysis Hybrid Systems,2009,3(3):251-258.
[4] AHMAD B,SIVASUNDARAM S.Existence of solutions for impulsive integral boundary value problems of fractional order[J].Nonlinear Analysis:Hybrid Systems,2010,4(1):134-141.
[5] REHMAN M,ELOE P W.Existence and uniqueness of solutions for impulsive fractional differential equations[J].Applied Mathematics and Computation,2013,224:422-431.
[6] WANG J R,ZHOU Y,FEC M.On recent developments in the theory of boundary value problems for impulsive fractional differential equations[J].Computers & Mathematics with Applications,2012,64(10):3008-3020.
[7] WANG X.Impulsive boundary value problem for nonlinear differential equations of fractional order[J].Computers & Mathematics with Applications,2011,62(5):2383-2391.
[8] ZHOU J,FENG M.Green's function for Sturm-Liouville-type boundary value problems of fractional order impulsive differential equations and its application[J].Boundary Value Problems,2014,2014(1):69.
[9] ZHOU W X,LIU X.Existence of solution to a class of boundary value problem for impulsive fractional differential equations[J].Advances in Difference Equations,2014,2014(1):12.
[10] KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and applications of fractional differential equations[M].North-Holland Math.Stud,2006,204.
[11] WANG J R,ZHOU Y,LIN Z.On a new class of impulsive fractional differential equations[J].Applied Mathematics and Computation,2014,242:649-657.
[12] 熊淑雪,孙峪怀.非线性分数阶Sharma-Tasso-Olver方程新的精确解[J].云南民族大学学报(自然科学版),2018,27(3):202-205.
[2] ZHAO K,GONG P.Positive solutions for impulsive fractional differential equations with generalizedperiodic boundary value conditions[J].Advances in Difference Equations,2014,2014(1):255.
[3] AHMAD B,SIVASUNDARAM S.Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations[J].Nonlinear Analysis Hybrid Systems,2009,3(3):251-258.
[4] AHMAD B,SIVASUNDARAM S.Existence of solutions for impulsive integral boundary value problems of fractional order[J].Nonlinear Analysis:Hybrid Systems,2010,4(1):134-141.
[5] REHMAN M,ELOE P W.Existence and uniqueness of solutions for impulsive fractional differential equations[J].Applied Mathematics and Computation,2013,224:422-431.
[6] WANG J R,ZHOU Y,FEC M.On recent developments in the theory of boundary value problems for impulsive fractional differential equations[J].Computers & Mathematics with Applications,2012,64(10):3008-3020.
[7] WANG X.Impulsive boundary value problem for nonlinear differential equations of fractional order[J].Computers & Mathematics with Applications,2011,62(5):2383-2391.
[8] ZHOU J,FENG M.Green's function for Sturm-Liouville-type boundary value problems of fractional order impulsive differential equations and its application[J].Boundary Value Problems,2014,2014(1):69.
[9] ZHOU W X,LIU X.Existence of solution to a class of boundary value problem for impulsive fractional differential equations[J].Advances in Difference Equations,2014,2014(1):12.
[10] KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and applications of fractional differential equations[M].North-Holland Math.Stud,2006,204.
[11] WANG J R,ZHOU Y,LIN Z.On a new class of impulsive fractional differential equations[J].Applied Mathematics and Computation,2014,242:649-657.
[12] 熊淑雪,孙峪怀.非线性分数阶Sharma-Tasso-Olver方程新的精确解[J].云南民族大学学报(自然科学版),2018,27(3):202-205.