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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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 40; no. 17; pp. 6138 - 6146
Main Author: Plekhanova, Marina V.
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 30.11.2017
Subjects:
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)
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary: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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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3830