Fractional differential equations with dependence on the Caputo-Katugampola derivative
In this paper we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo–Kat...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2016
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10773/16198 |
| Country: | Portugal |
| Oai: | oai:ria.ua.pt:10773/16198 |
| Summary: | In this paper we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy type problem, with dependence on the Caputo–Katugampola derivative, is proven. A decomposition formula for the Caputo–Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation. |
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