On the distributional fractional derivative: From unidimensional to multidimensional
In this paper, we use the generalized notions of Riemann–Liouville (fractional calculus with respect to a regular function) to extend the definitions of fractional integration and derivative from the functional sense to the distributional sense. First, we give some properties of fractional integral...
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| Published in | Mathematical methods in the applied sciences Vol. 47; no. 15; pp. 12350 - 12365 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.10.2024
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| Online Access | Get full text |
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| Summary: | In this paper, we use the generalized notions of Riemann–Liouville (fractional calculus with respect to a regular function) to extend the definitions of fractional integration and derivative from the functional sense to the distributional sense. First, we give some properties of fractional integral and derivative for the functions infinitely differentiable with compact support. Then, we define the weak derivative, as well as the integral and derivative of a distribution with compact support, and the integral and derivative of a distribution using the convolution product. Then, we generalize those concepts from the unidimensional to the multidimensional case. Finally, we propose the definitions of some usual differential operators. |
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| ISSN: | 0170-4214 1099-1476 |
| DOI: | 10.1002/mma.10203 |