On the Aronszajn property for an implicit differential equation of fractional order (Q606469)
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scientific article; zbMATH DE number 5816830
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Aronszajn property for an implicit differential equation of fractional order |
scientific article; zbMATH DE number 5816830 |
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On the Aronszajn property for an implicit differential equation of fractional order (English)
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17 November 2010
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The paper is concerned with existence theory for a fractional differential equation of the form \[ D^\beta x =g(t,x,D^\beta x); \quad x(0)=x_0, \] where the fractional derivative is taken in the Caputo sense. The main result of the paper shows that under appropriate conditions, the set of solutions to the equation is homeomorphic to the intersection of a decreasing sequence of compact absolute retracts.
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Caputo derivative
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existence theory
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implicit equation
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fractional calculus
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