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Journal of the Belarusian State University. Mathematics and Informatics, 2018, Volume 3, Pages 39–45
(Mi bgumi118)
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Differential equations and Optimal control
On continuous solutions of the Cauchy problem for equations of fractional order
P. P. Zabreiko, S. Ponomareva Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
Abstract:
It is studied the nonlocal conditions of solving Cauchy-type problem for fractional differential equations with Riemann – Liouville derivatives in some special function space. The Cauchy problem is reduced to a the finding fixed point of an integral operator A, then is constructed an invariant set for $A$ (the «shift» of a ball from the space of continuous functions, and then it is applied the Schauder anf Banach – Caccioppoli fixed point principles. As a result, the conditions of solvability and unique solvability for the Cauchy problem under consideration are given.
Keywords:
Cauchy problem; fractional Riemann – Liouville derivative; the Schauder fixed point principle; the Banach – Ñaccioppoli fixed point principle.
Received: 11.06.2018
Citation:
P. P. Zabreiko, S. Ponomareva, “On continuous solutions of the Cauchy problem for equations of fractional order”, Journal of the Belarusian State University. Mathematics and Informatics, 3 (2018), 39–45
Linking options:
https://www.mathnet.ru/eng/bgumi118 https://www.mathnet.ru/eng/bgumi/v3/p39
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Abstract page: | 52 | Full-text PDF : | 28 | References: | 17 |
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