On evolutionary equations with material laws containing fractional integrals |
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| Authors: | Rainer Picard Sascha Trostorff Marcus Waurick |
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| Affiliation: | Institut für Analysis,Fachrichtung Mathematik, Technische Universit?t Dresden, Germany |
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| Abstract: | A well‐posedness result for a time‐shift invariant class of evolutionary operator equations involving material laws with fractional time‐integrals of order α ? ]0, 1 is considered. The fractional derivatives are defined via a function calculus for the (time‐)derivative established as a normal operator in a suitable L2 type space. Employing causality, we show that the fractional derivatives thus obtained coincide with the Riemann‐Liouville fractional derivative. We exemplify our results by applications to a fractional Fokker‐Planck equation, equations describing super‐diffusion and sub‐diffusion processes, and a Kelvin‐Voigt type model in fractional visco‐elasticity. Moreover, we elaborate a suitable perspective to deal with initial boundary value problems. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | fractional derivatives fractional integrals evolutionary equations visco‐elasticity Kelvin– Voigt model fractional Fokker– Planck equation sub‐diffusion super‐diffusion causality |
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