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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |