Initial value problems should not be associated to fractional model descriptions whatever the derivative definition used
Keyword(s):
<abstract> <p>The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a time fractional model and if initial conditions are taken into account. The demonstration is done using simple examples (or counterexamples). The analysis is extended to the Riemann-Liouville and Grünwald-Letnikov definitions. These results thus question the validity of results produced in the field of time fractional model analysis in which initial conditions are involved.</p> </abstract>
2008 ◽
Vol 19
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pp. 701-715
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2013 ◽
Vol 2013
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pp. 1-6
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1998 ◽
Vol 67
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pp. 1157-1162
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1995 ◽
Vol 301
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pp. 269-294
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1975 ◽
Vol 18
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pp. 577-585
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