Weighted Cauchy problem: fractional versus integer order
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Integral Equations and Applications |
| MU Faculty or unit | |
| 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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