Abstract:
We prove the uniform correctness of a Cauchy-type problem with two fractional derivatives and a bounded operator A. We propose a criterion for the uniform correctness of unbounded operator A.
Keywords:
equations of fractional order, uniform correctness of Cauchy-type problem, resolving operator.
This publication is cited in the following 6 articles:
V. E. Fedorov, A. S. Avilovich, “A Cauchy type problem for a degenerate equation with the Riemann–Liouville derivative in the sectorial case”, Siberian Math. J., 60:2 (2019), 359–372
V. E. Fedorov, M. V. Plekhanova, R. R. Nazhimov, “Degenerate linear evolution equations with the Riemann–Liouville fractional derivative”, Siberian Math. J., 59:1 (2018), 136–146
Marina V. Plekhanova, “Degenerate distributed control systems with fractional time derivative”, Ural Math. J., 2:2 (2016), 58–71
Furati Kh.M., “Bounds on the Solution of a Cauchy-Type Problem Involving a Weighted Sequential Fractional Derivative”, Fract. Calc. Appl. Anal., 16:1, SI (2013), 171–188
Furati Kh.M., “A Cauchy-Type Problem Involving a Weighted Sequential Derivative in the Space of Integrable Functions”, Comput. Math. Appl., 66:5 (2013), 883–891
Furati Kh.M., “A Cauchy-Type Problem with a Sequential Fractional Derivative in the Space of Continuous Functions”, Bound. Value Probl., 2012, 58
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