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@article{1838218, author = {Morales Macias, Maria Guadalupe and Došlá, Zuzana}, article_number = {4}, doi = {http://dx.doi.org/10.1216/jie.2021.33.497}, keywords = {weighted Cauchy problem; unweighted Cauchy problem; Volterra integral equation; fractional differential equations; Riemann–Liouville fractional derivative; Lipschitz operator}, language = {eng}, issn = {0897-3962}, journal = {Journal of Integral Equations and Applications}, title = {Weighted Cauchy problem: fractional versus integer order}, url = {https://doi.org/jie.2021.33-4}, volume = {33}, year = {2021} }
TY - JOUR ID - 1838218 AU - Morales Macias, Maria Guadalupe - Došlá, Zuzana PY - 2021 TI - Weighted Cauchy problem: fractional versus integer order JF - Journal of Integral Equations and Applications VL - 33 IS - 4 SP - 497-509 EP - 497-509 PB - Rocky Mountain Mathematics Consortium SN - 08973962 KW - weighted Cauchy problem KW - unweighted Cauchy problem KW - Volterra integral equation KW - fractional differential equations KW - Riemann–Liouville fractional derivative KW - Lipschitz operator UR - https://doi.org/jie.2021.33-4 N2 - This work is devoted to the solvability of the weighted Cauchy problem for fractional differential equations of arbitrary order, considering the Riemann–Liouville derivative. We show the equivalence between the weighted Cauchy problem and the Volterra integral equation in the space of Lebesgue integrable functions. Finally, we point out some discrepancies between the solutions for fractional and integer order case. ER -
MORALES MACIAS, Maria Guadalupe a Zuzana DOŠLÁ. Weighted Cauchy problem: fractional versus integer order. \textit{Journal of Integral Equations and Applications}. Rocky Mountain Mathematics Consortium, 2021, roč.~33, č.~4, s.~497-509. ISSN~0897-3962. Dostupné z: https://dx.doi.org/10.1216/jie.2021.33.497.
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