Distributed Order Derivatives and Relaxation Patterns

Details Distributed Order Derivatives and Relaxation Patterns Distributed Order Derivatives and Relaxation Patterns

2009-05-05

arxiv.org/abs/0905.0616v1

Physics

Mathematical Physics

Scientific paper

We consider equations of the form $(D_{(\rho)}u)(t)=-\lambda u(t)$, $t>0$, where $\lambda >0$, $D_{(\rho)}$ is a distributed order derivative, that is the Caputo-Dzhrbashyan fractional derivative of order $\alpha$, integrated in $\alpha\in (0,1)$ with respect to a positive measure $\rho$. Such equations are used for modeling anomalous, non-exponential relaxation processes. In this work we study asymptotic behavior of solutions of the above equation, depending on properties of the measure $\rho$.

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