Publication details

Weighted Cauchy problem: fractional versus integer order

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Authors

MORALES MACIAS Maria Guadalupe DOŠLÁ Zuzana

Year of publication 2021
Type Article in Periodical
Magazine / Source Journal of Integral Equations and Applications
MU Faculty or unit

Faculty of Science

Citation
web https://doi.org/jie.2021.33-4
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
Description 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.
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