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On the separation of solutions of fractional differential equations

  • Consider two different solutions of a first-order differential equation. Under rather general conditions we know that these two functions are separated from each other, i.e. their graphs never meet or even cross each other. We ask whether such a result is true for Caputo-type fractional differential equations as well. We can give a partial answer that is positive in some situations and negative under different assumptions. For the remaining cases we state a conjecture and explain why we believe in it. A key ingredient of the analysis is a result concerning the existence of zeros of the solutions of a class of Volterra equations.

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Metadaten
Author:Kai Diethelm
Persistent identifier:https://www.diogenes.bg/fcaa/volume11/fcaa113/KDiethelm_fcaa113.pdf
Parent Title (English):Fractional Calculus and Applied Analysis
Document Type:Article
Language:English
Year of publication:2008
Release Date:2023/08/09
Volume:11
First Page:259
Last Page:268
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