Well-posedness of abstract distributed-order fractional diffusion equations

Junxiong Jia; Jigen Peng; Kexue Li

doi:10.3934/cpaa.2014.13.605

Article Contents

2014, Volume 13, Issue 2: 605-621. Doi: 10.3934/cpaa.2014.13.605

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Well-posedness of abstract distributed-order fractional diffusion equations

1.
School of Mathematics and Statistics, Ministry of Education Key Lab for Intelligent Networks and Network Security, Xi'an Jiaotong University, Xi'an 710049

Received: November 30, 2012

Revised: July 31, 2013

Published: February 2014

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Abstract

In this paper, based on distributed-order fractional diffusion equation we propose the distributed-order fractional abstract Cauchy problem (DFACP) and study the well-posedness of DFACP. Using functional calculus technique, we prove that the general distributed-order fractional operator generates a bounded analytic $\alpha$-times resolvent operator family or a $C_0$-semigroup under some suitable conditions. In addition, we reveal the relation between two $\alpha$-times resolvent families generated by the sectorial operator $A$ and the special distributed-order fractional operator, $p_1A^{\beta_1}+ p_2A^{\beta_2}+\ldots +p_nA^{\beta_n}$, respectively.

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Mathematics Subject Classification: Primary: 26A33; Secondary: 47D06.

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