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@article{1686737, author = {Morales Macias, Maria Guadalupe and Došlá, Zuzana and Mendoza, Francisco J.}, article_location = {Springfield}, article_number = {2}, 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}, language = {eng}, issn = {2688-1594}, journal = {Electronic Research Archive}, title = {Riemann-Liouville derivative over the space of integrable distributions}, url = {http://www.aimsciences.org/article/doi/10.3934/era.2020030}, volume = {28}, year = {2020} }
TY - JOUR ID - 1686737 AU - Morales Macias, Maria Guadalupe - Došlá, Zuzana - Mendoza, Francisco J. PY - 2020 TI - Riemann-Liouville derivative over the space of integrable distributions JF - Electronic Research Archive VL - 28 IS - 2 SP - 567-587 EP - 567-587 PB - Amer Inst Mathematical Sciences SN - 26881594 KW - Distributional Henstock-Kurzweil integral KW - convolution KW - Henstock-Kurzweil integrable distribution KW - Riemann-Liouville fractional differential operator KW - Riemann-Liouville fractional integral operator UR - http://www.aimsciences.org/article/doi/10.3934/era.2020030 L2 - http://www.aimsciences.org/article/doi/10.3934/era.2020030 N2 - 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. ER -
MORALES MACIAS, Maria Guadalupe, Zuzana DOŠLÁ a Francisco J. MENDOZA. Riemann-Liouville derivative over the space of integrable distributions. \textit{Electronic Research Archive}. Springfield: Amer Inst Mathematical Sciences, 2020, roč.~28, č.~2, s.~567-587. ISSN~2688-1594. Dostupné z: https://dx.doi.org/10.3934/era.2020030.
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