多基点分数阶微分方程脉冲边值问题解的存在性
|
摘要
该文研究了α(∈(1,2))阶非线性多基点分数微分方程脉冲边值问题解的存在性,利用不动点定理在较弱条件下得到了解的存在性定理,并通过三个实例验证了解的存在性.
In this paper, we study the existence of solutions for impulsive boundary value problem for nonlinear multiple base points differential equations of fractional order α∈(1,2).By using some well-known fixed point theorem, we obtain an existence result on solution under the weak assumption. Three examples are given to illustrate the existence theorems.
In this paper, we study the existence of solutions for impulsive boundary value problem for nonlinear multiple base points differential equations of fractional order α∈(1,2).By using some well-known fixed point theorem, we obtain an existence result on solution under the weak assumption. Three examples are given to illustrate the existence theorems.
引文
[1]Tarasov V E.Fractional Dynamics:Applications of Fractional Calculus to Dynamics of Particles,Fields and Media.Beijing:Higher Education Press,2010
[2]Garrapa R,Popolizio M.On accurate product integration rules for linear fractional differential equations.J Comput Appl Math,2011,235:1085-1097
[3]Kilbas A A,Srivastava H M,Trujillo J J.Theory and Applications of Fractional Differential Equations.Amsterdam:Elsevier Science,2006
[4]Agarwal R P,Benchohra M,Slimani B A.Existence results for differential equations with fractional order and impulses.Memoirs Differ Equ Math Phys,2008,44:1-21
[5]Zhou Y.Basic Theory of Fractional Differential Equations.Singapore:World Scientific Publishing,2014
[6]Povstenko Y.Time-fractional thermoelasticity problem for a sphere subjected to the heat flux.Appl Math Comput,2015,257:327-334
[7]Pu X.Dynamics of a fractional hydrodynamical equation for the Heisenberg paramagnet.Appl Math Comput,2015,257:213-229
[8]Wang J,Zhou Y,Feckan M.On recent developments in the theory of boundary value problems for impulsive fractional differential equations.Comput Math Appl,2012,64:3008-3020
[9]Liu Y.Existence of solutions for impulsive differential models on half lines involving Caputo fractional derivatives.Commun Nonlinear Sci Numer Simulat,2013,18:2604-2625
[10]Liu Y J,Ahmad B.A study of impulsive multiterm fractional differential equations with single and multiple base points and applications.Sci World J,2014,2014:Article ID:194346
[11]Lan K Q,Lin W.Positive solutions of systems of Caputo fractional differentail equations.Commun Appl Anal,2013,17:61-68
[12]Wang G,Ahmad B,Zhang L.Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions.Comput Math Appl,2011,62:1389-1397
[13]Li X,Chen F.Generalized anti-periodic boundary value problems of impulsive fractional differential equations.Commun Nonlinear Sci Numer Simulat,2013,18:28-41
[14]Tian Y,Bai Z.Existence results for the three-point impulsive boundary value problem involving fractional differential equations.Comput Math Appl,2010,59:2601-2609
[15]Ashyralyev A,Sharifov Y A.Existence and uniqueness of solutions for the system of nonlinear fractional differential equations with nonlocal and integral boundary conditions.Abstr Appl Anal,2012,2012:Art No:594802
[16]Bai Z,Lu H.Positive solutions for boundary value problem of nonlinear fractional differ ential equations.J Math Anal Appl,2005,311:459-505
[17]Kaufmann E R,Mboumi E.Positive solutions of a boundary value problem for a nonlinear fractional differential equation.Electron J Qual Theory Differ Equ,2008,3:1-11
[2]Garrapa R,Popolizio M.On accurate product integration rules for linear fractional differential equations.J Comput Appl Math,2011,235:1085-1097
[3]Kilbas A A,Srivastava H M,Trujillo J J.Theory and Applications of Fractional Differential Equations.Amsterdam:Elsevier Science,2006
[4]Agarwal R P,Benchohra M,Slimani B A.Existence results for differential equations with fractional order and impulses.Memoirs Differ Equ Math Phys,2008,44:1-21
[5]Zhou Y.Basic Theory of Fractional Differential Equations.Singapore:World Scientific Publishing,2014
[6]Povstenko Y.Time-fractional thermoelasticity problem for a sphere subjected to the heat flux.Appl Math Comput,2015,257:327-334
[7]Pu X.Dynamics of a fractional hydrodynamical equation for the Heisenberg paramagnet.Appl Math Comput,2015,257:213-229
[8]Wang J,Zhou Y,Feckan M.On recent developments in the theory of boundary value problems for impulsive fractional differential equations.Comput Math Appl,2012,64:3008-3020
[9]Liu Y.Existence of solutions for impulsive differential models on half lines involving Caputo fractional derivatives.Commun Nonlinear Sci Numer Simulat,2013,18:2604-2625
[10]Liu Y J,Ahmad B.A study of impulsive multiterm fractional differential equations with single and multiple base points and applications.Sci World J,2014,2014:Article ID:194346
[11]Lan K Q,Lin W.Positive solutions of systems of Caputo fractional differentail equations.Commun Appl Anal,2013,17:61-68
[12]Wang G,Ahmad B,Zhang L.Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions.Comput Math Appl,2011,62:1389-1397
[13]Li X,Chen F.Generalized anti-periodic boundary value problems of impulsive fractional differential equations.Commun Nonlinear Sci Numer Simulat,2013,18:28-41
[14]Tian Y,Bai Z.Existence results for the three-point impulsive boundary value problem involving fractional differential equations.Comput Math Appl,2010,59:2601-2609
[15]Ashyralyev A,Sharifov Y A.Existence and uniqueness of solutions for the system of nonlinear fractional differential equations with nonlocal and integral boundary conditions.Abstr Appl Anal,2012,2012:Art No:594802
[16]Bai Z,Lu H.Positive solutions for boundary value problem of nonlinear fractional differ ential equations.J Math Anal Appl,2005,311:459-505
[17]Kaufmann E R,Mboumi E.Positive solutions of a boundary value problem for a nonlinear fractional differential equation.Electron J Qual Theory Differ Equ,2008,3:1-11