Riemann-Liouville derivative over the space of integrable distributions
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Electronic Research Archive |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.aimsciences.org/article/doi/10.3934/era.2020030 |
| Doi | http://dx.doi.org/10.3934/era.2020030 |
| Keywords | Distributional Henstock-Kurzweil integral; convolution; Henstock-Kurzweil integrable distribution; Riemann-Liouville fractional differential operator; Riemann-Liouville fractional integral operator |
| Description | In this paper, we generalize the Riemann-Liouville differential and integral operators on the space of Henstock-Kurzweil integrable distributions, DHK. We obtain new fundamental properties of the fractional derivatives and integrals, a general version of the fundamental theorem of fractional calculus, semigroup property for the Riemann-Liouville integral operators and relations between the Riemann-Liouville integral and differential operators. Also, we achieve a generalized characterization of the solution for the Abel integral equation. Finally, we show relations for the Fourier transform of fractional derivative and integral. These results are based on the properties of the distributional Henstock-Kurzweil integral and convolution. |
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