In this paper, we generalize the Riemann-Liouville differential and integral operators on the space of Henstock-Kurzweil integrable distributions, . 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.
Citation: María Guadalupe Morales, Zuzana Došlá, Francisco J. Mendoza. Riemann-Liouville derivative over the space of integrable distributions[J]. Electronic Research Archive, 2020, 28(2): 567-587. doi: 10.3934/era.2020030
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In this paper, we generalize the Riemann-Liouville differential and integral operators on the space of Henstock-Kurzweil integrable distributions, . 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.
Dear Editorial Board Members and Readers:
It is my pleasure to share with you the year-end report for AIMS Environmental Science for 2021. The journal continues to improve its quality as indicated by steady increases in the number of manuscripts received and the number of articles published over the past three years. We have received 202 submissions with 40 published online. The top read article received more than 15980 downloads.
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Yifeng Wang, Ph.D.
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María Guadalupe Morales, Zuzana Došlá, Francisco J. Mendoza. Riemann-Liouville derivative over the space of integrable distributions[J]. Electronic Research Archive, 2020, 28(2): 567-587. doi: 10.3934/era.2020030
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