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Nonlinear equations with degenerate operator at fractional Caputo derivative

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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… Click to show full 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. 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.

Keywords: caputo derivative; operator fractional; nonlinear equations; fractional caputo; degenerate operator

Journal Title: Mathematical Methods in The Applied Sciences
Year Published: 2017

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