Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales
The Δ-power function and fractional Δ-integrals and fractional Δ-differential are defined, and then the definitions and properties of Δ-Mittag-Leffler function are given. The properties of fractional Δ-integrals and fractional Δ-differential on time scales are discussed in detail. After that, the e...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/401596 |
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| _version_ | 1832566903723261952 |
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| author | Jiang Zhu Ying Zhu |
| author_facet | Jiang Zhu Ying Zhu |
| author_sort | Jiang Zhu |
| collection | DOAJ |
| description | The Δ-power function and fractional Δ-integrals and fractional Δ-differential are defined, and then the
definitions and properties of Δ-Mittag-Leffler function are given.
The properties of fractional Δ-integrals and fractional Δ-differential on time scales are discussed in detail. After that, the
existence of the solution and the dependency of the solution upon the
initial value for Cauchy type problem with fractional Δ-derivative
are studied. Also the explicit solutions to homogeneous fractional Δ-differential equations and nonhomogeneous fractional Δ-differential
equations are derived by using Laplace transform method. |
| format | Article |
| id | doaj-art-7cf0c85507e94125babe30e933c0951e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7cf0c85507e94125babe30e933c0951e2025-02-03T01:02:47ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/401596401596Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time ScalesJiang Zhu0Ying Zhu1School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, ChinaSchool of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, ChinaThe Δ-power function and fractional Δ-integrals and fractional Δ-differential are defined, and then the definitions and properties of Δ-Mittag-Leffler function are given. The properties of fractional Δ-integrals and fractional Δ-differential on time scales are discussed in detail. After that, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Δ-derivative are studied. Also the explicit solutions to homogeneous fractional Δ-differential equations and nonhomogeneous fractional Δ-differential equations are derived by using Laplace transform method.http://dx.doi.org/10.1155/2013/401596 |
| spellingShingle | Jiang Zhu Ying Zhu Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales Abstract and Applied Analysis |
| title | Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales |
| title_full | Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales |
| title_fullStr | Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales |
| title_full_unstemmed | Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales |
| title_short | Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales |
| title_sort | fractional cauchy problem with riemann liouville fractional delta derivative on time scales |
| url | http://dx.doi.org/10.1155/2013/401596 |
| work_keys_str_mv | AT jiangzhu fractionalcauchyproblemwithriemannliouvillefractionaldeltaderivativeontimescales AT yingzhu fractionalcauchyproblemwithriemannliouvillefractionaldeltaderivativeontimescales |