A Gronwall inequality for a general Caputo fractional operator
In this paper we present a new type of fractional operator, which is a generalization of the Caputo and Caputo–Hadamard fractional derivative operators. We study some properties of the operator, namely we prove that it is the inverse operation of a generalized fractional integral. A relation between...
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| Format: | article |
| Language: | eng |
| Published: |
1000
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| Online Access: | http://hdl.handle.net/10773/18541 |
| Country: | Portugal |
| Oai: | oai:ria.ua.pt:10773/18541 |
| Summary: | In this paper we present a new type of fractional operator, which is a generalization of the Caputo and Caputo–Hadamard fractional derivative operators. We study some properties of the operator, namely we prove that it is the inverse operation of a generalized fractional integral. A relation between this operator and a Riemann–Liouville type is established. We end with a fractional Gronwall inequality type, which is useful to compare solutions of fractional differential equations. |
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