Nonlinear equations with degenerate operator at fractional Caputo derivative
At first, the existence of a unique solution for the Cauchy problem to nondegenerate fractional differential equation was proved. These results were used for research of the unique solvability for the initial Cauchy and Showalter–Sidorov problems to differential equations in Banach spaces with degen...
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| Published in: | Mathematical methods in the applied sciences Vol. 40; no. 17; pp. 6138 - 6146 |
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| Format: | Journal Article |
| Language: | English |
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Freiburg
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30.11.2017
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| ISSN: | 0170-4214, 1099-1476 |
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| Abstract | At first, the existence of a unique solution for the Cauchy problem to nondegenerate fractional differential equation was proved. These results were used for research of the unique solvability for the initial Cauchy and Showalter–Sidorov problems to differential equations in Banach spaces with degenerate operator at fractional Caputo derivative in linear and nonlinear cases. results are applied to the research of an initial boundary value problem for time‐fractional order Oskolkov system of equations. Copyright © 2016 John Wiley & Sons, Ltd. |
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| AbstractList | At first, the existence of a unique solution for the Cauchy problem to nondegenerate fractional differential equation was proved. These results were used for research of the unique solvability for the initial Cauchy and Showalter–Sidorov problems to differential equations in Banach spaces with degenerate operator at fractional Caputo derivative in linear and nonlinear cases. results are applied to the research of an initial boundary value problem for time‐fractional order Oskolkov system of equations. Copyright © 2016 John Wiley & Sons, Ltd. At first, the existence of a unique solution for the Cauchy problem to nondegenerate fractional differential equation was proved. These results were used for research of the unique solvability for the initial Cauchy and Showalter-Sidorov problems to differential equations in Banach spaces with degenerate operator at fractional Caputo derivative in linear and nonlinear cases. Abstract results are applied to the research of an initial boundary value problem for time-fractional order Oskolkov system of equations. Copyright © 2016 John Wiley & Sons, Ltd. |
| Author | Plekhanova, Marina V. |
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| Cites_doi | 10.3103/S1066369X15010065 10.1002/mma.2935 10.1137/0506004 10.4310/DPDE.2014.v11.n1.a4 10.1134/S003744661504014X 10.1002/mma.3151 10.1515/9783110915501 10.1007/s10957-012-0174-7 10.1007/s10958-010-9981-2 10.1007/BF01139992 10.1002/mma.1582 10.1134/S0012266113120112 10.1134/S0012266113030087 |
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| References | 2013; 19 2015; 56 2015; 12 2015; 59 2015; 38 2013; 49 2001 2010; 168 1984; 35 2013; 156 2014; 37 1988; 179 2003 2012; 15 2012; 35 2014; 11 1975; 6 1999 Favini A (e_1_2_9_2_1) 1999 e_1_2_9_11_1 e_1_2_9_10_1 Xinwei Y (e_1_2_9_8_1) 2012; 35 e_1_2_9_13_1 Gordievskikh DM (e_1_2_9_14_1) 2015; 12 Ivanova ND (e_1_2_9_20_1) 2012; 15 e_1_2_9_7_1 e_1_2_9_6_1 e_1_2_9_5_1 e_1_2_9_4_1 e_1_2_9_3_1 Fedorov VE (e_1_2_9_12_1) 2013; 19 Oskolkov AP (e_1_2_9_15_1) 1988; 179 e_1_2_9_9_1 e_1_2_9_17_1 e_1_2_9_16_1 e_1_2_9_19_1 e_1_2_9_18_1 |
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| SubjectTerms | Boundary value problems Cauchy problems degenerate fractional differential equation Differential equations fractional partial differential equations Mathematical analysis Nonlinear equations nonlinear equations in abstract spaces nonlinear evolution equations Operators (mathematics) |
| Title | Nonlinear equations with degenerate operator at fractional Caputo derivative |
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