Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions
In this paper, we consider a class of boundary value problems of nonlinear fractional differential equation with integral boundary conditions. By applying the monotone iterative method and some inequalities associated with Green’s function, we obtain the existence of minimal and maximal positive sol...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/6738379 |
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| _version_ | 1832547075842113536 |
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| author | Min Li Jian-Ping Sun Ya-Hong Zhao |
| author_facet | Min Li Jian-Ping Sun Ya-Hong Zhao |
| author_sort | Min Li |
| collection | DOAJ |
| description | In this paper, we consider a class of boundary value problems of nonlinear fractional differential equation with integral boundary conditions. By applying the monotone iterative method and some inequalities associated with Green’s function, we obtain the existence of minimal and maximal positive solutions and establish two iterative sequences for approximating the solutions to the above problem. It is worth mentioning that these iterative sequences start off with zero function or linear function, which is useful and feasible for computational purpose. An example is also included to illustrate the main result of this paper. |
| format | Article |
| id | doaj-art-4937857acdc443fbb246a9a78e146e9d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4937857acdc443fbb246a9a78e146e9d2025-02-03T06:46:06ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/67383796738379Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary ConditionsMin Li0Jian-Ping Sun1Ya-Hong Zhao2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaIn this paper, we consider a class of boundary value problems of nonlinear fractional differential equation with integral boundary conditions. By applying the monotone iterative method and some inequalities associated with Green’s function, we obtain the existence of minimal and maximal positive solutions and establish two iterative sequences for approximating the solutions to the above problem. It is worth mentioning that these iterative sequences start off with zero function or linear function, which is useful and feasible for computational purpose. An example is also included to illustrate the main result of this paper.http://dx.doi.org/10.1155/2020/6738379 |
| spellingShingle | Min Li Jian-Ping Sun Ya-Hong Zhao Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions Discrete Dynamics in Nature and Society |
| title | Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions |
| title_full | Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions |
| title_fullStr | Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions |
| title_full_unstemmed | Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions |
| title_short | Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions |
| title_sort | positive solutions for bvp of fractional differential equation with integral boundary conditions |
| url | http://dx.doi.org/10.1155/2020/6738379 |
| work_keys_str_mv | AT minli positivesolutionsforbvpoffractionaldifferentialequationwithintegralboundaryconditions AT jianpingsun positivesolutionsforbvpoffractionaldifferentialequationwithintegralboundaryconditions AT yahongzhao positivesolutionsforbvpoffractionaldifferentialequationwithintegralboundaryconditions |