一类非线性分数阶q-导数方程的正解
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摘要
利用不动点理论和算子方程Ax=λx正解的一些性质,研究了一类非线性分数阶q-导数方程积分边值问题正解的存在唯一性,并且给出正解依赖与参数λ的一些性质。
We use the fixed point theory and some properties of the positive solutions for the operator equation to study the existence and uniqueness of the positive solution for a class of nonlinear fractional q-derivative equations with integral boundary value problems.Moreover we give some property of positive solutions to the boundary value problem depended on the parameter.
We use the fixed point theory and some properties of the positive solutions for the operator equation to study the existence and uniqueness of the positive solution for a class of nonlinear fractional q-derivative equations with integral boundary value problems.Moreover we give some property of positive solutions to the boundary value problem depended on the parameter.
引文
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[3]Shah K,Wang J,Khalil H,et al.Existence and Numerical Solutions of a Coupled System of Integral BVP for Fractional Differential Equations[J].Adv Differ Equ,2018,149:1-21.DOI:10.1186/s13662-018-1603-1.
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[7]Darzi R,Agheli B.Existence Results to Positive Solution of Fractional BVP with q-derivatives[J].Appl Math Comput,2016,55:353-367.DOI:10.1007/s12190-016-1040-9.
[8]Graef J R,Kong L.Positive Solutions for a Class of Higher Order Boundary Value Problems with Fractional q-derivatives[J].Appl Math Comput,2012,218:9682-9689.DOI:10.1016/j.amc.2012.03.006.
[9]Ahmad B,Ntouyas S K,Purnaras I K.Existence Results for Nonlocal Boundary Value Problems of Nonliner Fractional qdifference Equations[J].Adv Differ Equ,2012,55:1-21.DOI:10.1186/1687-2770-2012-55.
[10]Almeida R,Martins N.Existence Results for Fractional q-difference Equations of Orderα∈[2,3]with Three-point Boundary Conditions[J].Commun Nonlinear Sci and Numer Simul,2014,19(6):1675-1685.DOI:10.1016/j.cnsns.2013.10.018.
[11]Zhao Y L,Ye G B,Chen H B.Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractional q-Derivatives Equation[J].Abst Appl Anal,2013,Article ID 643571,1-12.DOI:10.1155/2013/643571.
[12]Zhai C B,Wang F.Properties of Positive Solutions for the Operator Equation Ax=λxand Applications to Fractional Differential Equations with Integral Boundary Conditions[J].Adv Differ Equ,2015,366:1-10.DOI:10.1186/s13662-015-0704-3.
[13]Wang J,Fe ckan M,Tian Y.Stability Analysis for a General Class of Non-instantaneous Impulsive Differential Equations[J].Mediterr J Math,2017,14(2):1-21.DOI:10.1007/s00009-017-0867-0.
[14]Zhai C B,Yang C,Zhang X.Positive Solutions for Nonlinear Operator Equations and Several Classes of Applications[J].Math Z,2010,266:43-63.DOI:10.1007/s00209-009-0553-4.
[15]Wang J R,Zhang Y R.On the Concept and Existence of Solutions for Fractional Impulsive Systems with Hadamard Derivatives[J].Appl Math Lett,2015,39:85-90.DOI:10.1016/j.aml.2014.08.015.
[16]郭大钧.非线性泛函分析[M].2版.济南:山东科技出版社,2001.
[2]Su C M,Sun J P,Zhao Y H.Existence and Uniqueness of Solutions for BVP of Nonlinear Fractional Differential Equation[J].International Journal of Differential Equations,2017,Article ID 4683581,1-7.DOI:10.1155/2017/4683581.
[3]Shah K,Wang J,Khalil H,et al.Existence and Numerical Solutions of a Coupled System of Integral BVP for Fractional Differential Equations[J].Adv Differ Equ,2018,149:1-21.DOI:10.1186/s13662-018-1603-1.
[4]Zhang X,Zhong Q.Triple Positive Solutions for Nonlocal Fractional Differential Equations with Singularities Both on Time and Space Variables[J].Appl Math Lett,2018,80:12-19.DOI:10.1016/j.aml.2017.12.022.
[5]Agarwal R P.Certain fractional q-integrals and q-derivatives[J].Proc Cambridge Philos Soc,1969,66:365-370.DOI:10.1017/S0305004100045060.
[6]Ferreira R A C.Positive Solutions for a Class of Boundary Value Problems with Fractional q-differences[J].Comput Math Appl,2011,61(2):367-373.DOI:10.1016/j.camwa.2010.11.012.
[7]Darzi R,Agheli B.Existence Results to Positive Solution of Fractional BVP with q-derivatives[J].Appl Math Comput,2016,55:353-367.DOI:10.1007/s12190-016-1040-9.
[8]Graef J R,Kong L.Positive Solutions for a Class of Higher Order Boundary Value Problems with Fractional q-derivatives[J].Appl Math Comput,2012,218:9682-9689.DOI:10.1016/j.amc.2012.03.006.
[9]Ahmad B,Ntouyas S K,Purnaras I K.Existence Results for Nonlocal Boundary Value Problems of Nonliner Fractional qdifference Equations[J].Adv Differ Equ,2012,55:1-21.DOI:10.1186/1687-2770-2012-55.
[10]Almeida R,Martins N.Existence Results for Fractional q-difference Equations of Orderα∈[2,3]with Three-point Boundary Conditions[J].Commun Nonlinear Sci and Numer Simul,2014,19(6):1675-1685.DOI:10.1016/j.cnsns.2013.10.018.
[11]Zhao Y L,Ye G B,Chen H B.Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractional q-Derivatives Equation[J].Abst Appl Anal,2013,Article ID 643571,1-12.DOI:10.1155/2013/643571.
[12]Zhai C B,Wang F.Properties of Positive Solutions for the Operator Equation Ax=λxand Applications to Fractional Differential Equations with Integral Boundary Conditions[J].Adv Differ Equ,2015,366:1-10.DOI:10.1186/s13662-015-0704-3.
[13]Wang J,Fe ckan M,Tian Y.Stability Analysis for a General Class of Non-instantaneous Impulsive Differential Equations[J].Mediterr J Math,2017,14(2):1-21.DOI:10.1007/s00009-017-0867-0.
[14]Zhai C B,Yang C,Zhang X.Positive Solutions for Nonlinear Operator Equations and Several Classes of Applications[J].Math Z,2010,266:43-63.DOI:10.1007/s00209-009-0553-4.
[15]Wang J R,Zhang Y R.On the Concept and Existence of Solutions for Fractional Impulsive Systems with Hadamard Derivatives[J].Appl Math Lett,2015,39:85-90.DOI:10.1016/j.aml.2014.08.015.
[16]郭大钧.非线性泛函分析[M].2版.济南:山东科技出版社,2001.