Strong analytic solutions of fractional Cauchy problems

Mijena, Jebessa; Nane, Erkan

doi:10.1090/S0002-9939-2014-11905-8

Strong analytic solutions of fractional Cauchy problems
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by Jebessa B. Mijena and Erkan Nane PDF

Proc. Amer. Math. Soc. 142 (2014), 1717-1731 Request permission

Abstract:

Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases a distributed order derivative can be used to model ultra-slow diffusion. We extend the results of Baeumer and Meerschaert in the single order fractional derivative case to the distributed order fractional derivative case. In particular, we develop strong analytic solutions of distributed order fractional Cauchy problems.

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