On continuous solutions of the Cauchy problem for equations of fractional order
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.
References
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Published
2019-01-19
Keywords:
Cauchy problem, fractional Riemann – Liouville derivative, the Schauder fixed point principle, the Banach – Сaccioppoli fixed point principle
How to Cite
Zabreiko, P. P., & Ponomareva, S. V. (2019). On continuous solutions of the Cauchy problem for equations of fractional order. Journal of the Belarusian State University. Mathematics and Informatics, 3, 39-45. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/1011
Section
Differential Equations and Optimal Control
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