A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations
We establish some sufficient conditions for the existence and uniqueness of positive solutions to a class of initial value problem for impulsive fractional differential equations involving the Caputo fractional derivative. Our analysis relies on a fixed point theorem for mixed monotone operators. Ou...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/745674 |
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| _version_ | 1850230787091202048 |
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| author | Jieming Zhang Chen Yang Chengbo Zhai |
| author_facet | Jieming Zhang Chen Yang Chengbo Zhai |
| author_sort | Jieming Zhang |
| collection | DOAJ |
| description | We establish some sufficient conditions for the existence and uniqueness of positive solutions to a class of initial value problem for impulsive fractional differential equations involving the Caputo fractional derivative. Our analysis relies on a fixed point theorem for mixed monotone operators. Our result can not only guarantee the existence of a unique positive solution but also be applied to construct an iterative scheme for approximating it. An example is given to illustrate our main result. |
| format | Article |
| id | doaj-art-1f9a44d48a3b4ec1a4aac55a5129ce5f |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-1f9a44d48a3b4ec1a4aac55a5129ce5f2025-08-20T02:03:46ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/745674745674A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential EquationsJieming Zhang0Chen Yang1Chengbo Zhai2Basic Course Department, Business College of Shanxi University, Taiyuan, Shanxi 030031, ChinaBasic Course Department, Business College of Shanxi University, Taiyuan, Shanxi 030031, ChinaSchool of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, ChinaWe establish some sufficient conditions for the existence and uniqueness of positive solutions to a class of initial value problem for impulsive fractional differential equations involving the Caputo fractional derivative. Our analysis relies on a fixed point theorem for mixed monotone operators. Our result can not only guarantee the existence of a unique positive solution but also be applied to construct an iterative scheme for approximating it. An example is given to illustrate our main result.http://dx.doi.org/10.1155/2013/745674 |
| spellingShingle | Jieming Zhang Chen Yang Chengbo Zhai A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations Discrete Dynamics in Nature and Society |
| title | A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations |
| title_full | A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations |
| title_fullStr | A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations |
| title_full_unstemmed | A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations |
| title_short | A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations |
| title_sort | mixed monotone operator method for the existence and uniqueness of positive solutions to impulsive caputo fractional differential equations |
| url | http://dx.doi.org/10.1155/2013/745674 |
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