Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations
We discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations (Dα-ρtDβ)x(t)=f(t,x(t),Dγx(t)), t∈(0,1) with boundary conditions x(0)=x0, x(1)=x1 or satisfying the initial conditions x(0)=0, x′(0)=1, where Dα denotes Caputo fractional derivative, ρ...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/632681 |
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| _version_ | 1850167675185004544 |
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| author | Azizollah Babakhani Dumitru Baleanu |
| author_facet | Azizollah Babakhani Dumitru Baleanu |
| author_sort | Azizollah Babakhani |
| collection | DOAJ |
| description | We discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations (Dα-ρtDβ)x(t)=f(t,x(t),Dγx(t)), t∈(0,1) with boundary conditions x(0)=x0, x(1)=x1 or satisfying the initial conditions x(0)=0, x′(0)=1, where Dα denotes Caputo fractional derivative, ρ is constant, 1<α<2, and 0<β+γ≤α. Schauder's fixed-point theorem was used to establish the existence of the solution. Banach contraction principle was used to show the uniqueness of the solution under certain conditions on f. |
| format | Article |
| id | doaj-art-e7606141346b4f7d8d841d03e098f56c |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e7606141346b4f7d8d841d03e098f56c2025-08-20T02:21:09ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/632681632681Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential EquationsAzizollah Babakhani0Dumitru Baleanu1Department of Mathematics, Faculty of Basic Science, Babol University of Technology, Babol 47148-71167, IranDepartment of Mathematics and Computer Science, Cankaya University, TurkeyWe discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations (Dα-ρtDβ)x(t)=f(t,x(t),Dγx(t)), t∈(0,1) with boundary conditions x(0)=x0, x(1)=x1 or satisfying the initial conditions x(0)=0, x′(0)=1, where Dα denotes Caputo fractional derivative, ρ is constant, 1<α<2, and 0<β+γ≤α. Schauder's fixed-point theorem was used to establish the existence of the solution. Banach contraction principle was used to show the uniqueness of the solution under certain conditions on f.http://dx.doi.org/10.1155/2012/632681 |
| spellingShingle | Azizollah Babakhani Dumitru Baleanu Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations Abstract and Applied Analysis |
| title | Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations |
| title_full | Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations |
| title_fullStr | Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations |
| title_full_unstemmed | Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations |
| title_short | Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations |
| title_sort | existence and uniqueness of solution for a class of nonlinear fractional order differential equations |
| url | http://dx.doi.org/10.1155/2012/632681 |
| work_keys_str_mv | AT azizollahbabakhani existenceanduniquenessofsolutionforaclassofnonlinearfractionalorderdifferentialequations AT dumitrubaleanu existenceanduniquenessofsolutionforaclassofnonlinearfractionalorderdifferentialequations |