The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations
In this paper, we research CFR fractional differential equations with the derivative of order 3<α<4. We prove existence and uniqueness theorems for CFR-type initial value problem. By Green’s function and its corresponding maximum value, we obtain the Lyapunov-type inequality of corresponding e...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/5875108 |
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| _version_ | 1832545720986501120 |
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| author | Xia Wang Run Xu |
| author_facet | Xia Wang Run Xu |
| author_sort | Xia Wang |
| collection | DOAJ |
| description | In this paper, we research CFR fractional differential equations with the derivative of order 3<α<4. We prove existence and uniqueness theorems for CFR-type initial value problem. By Green’s function and its corresponding maximum value, we obtain the Lyapunov-type inequality of corresponding equations. As for application, we study the eigenvalue problem in the sense of CFR. |
| format | Article |
| id | doaj-art-822084a29f4442e281d300e6238afd97 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-822084a29f4442e281d300e6238afd972025-02-03T07:24:53ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/58751085875108The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential EquationsXia Wang0Run Xu1School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, ChinaIn this paper, we research CFR fractional differential equations with the derivative of order 3<α<4. We prove existence and uniqueness theorems for CFR-type initial value problem. By Green’s function and its corresponding maximum value, we obtain the Lyapunov-type inequality of corresponding equations. As for application, we study the eigenvalue problem in the sense of CFR.http://dx.doi.org/10.1155/2018/5875108 |
| spellingShingle | Xia Wang Run Xu The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations Journal of Function Spaces |
| title | The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations |
| title_full | The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations |
| title_fullStr | The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations |
| title_full_unstemmed | The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations |
| title_short | The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations |
| title_sort | existence and uniqueness of solutions and lyapunov type inequality for cfr fractional differential equations |
| url | http://dx.doi.org/10.1155/2018/5875108 |
| work_keys_str_mv | AT xiawang theexistenceanduniquenessofsolutionsandlyapunovtypeinequalityforcfrfractionaldifferentialequations AT runxu theexistenceanduniquenessofsolutionsandlyapunovtypeinequalityforcfrfractionaldifferentialequations AT xiawang existenceanduniquenessofsolutionsandlyapunovtypeinequalityforcfrfractionaldifferentialequations AT runxu existenceanduniquenessofsolutionsandlyapunovtypeinequalityforcfrfractionaldifferentialequations |