Time distributed-order diffusion-wave equation. I. Volterra-type equation

被引：79

作者：

Atanackovic, Teodor M. ^{[2
]}

Pilipovic, Stevan ^{[3
]}

Zorica, Dusan ^{[1
]}

机构：

[1] Univ Novi Sad, Fac Civil Engn, Subotica 24000, Serbia

[2] Univ Novi Sad, Dept Mech, Fac Tech Sci, Novi Sad 21000, Serbia

[3] Univ Novi Sad, Dept Math, Fac Nat Sci & Math, Novi Sad 21000, Serbia

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2009年 / 465卷 / 2106期

关键词：

fractional derivative; distributed-order fractional derivative; diffusion-wave equation; Volterra equation; FRACTIONAL DIFFUSION; MULTIDIMENSIONAL SOLUTIONS;

D O I：

10.1098/rspa.2008.0445

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A single-order time-fractional diffusion-wave equation is generalized by introducing a time distributed-order fractional derivative and forcing term, while a Laplacian is replaced by a general linear multi-dimensional spatial differential operator. The obtained equation is ( in the case of the Laplacian) called a time distributed-order diffusion-wave equation. We analyse a Cauchy problem for such an equation by means of the theory of an abstract Volterra equation. The weight distribution, occurring in the distributed-order fractional derivative, is specified as the sum of the Dirac distributions and the existence and uniqueness of solutions to the Cauchy problem, and the corresponding Volterra-type equation were proven for a general linear spatial differential operator, as well as in the special case when the operator is Laplacian.

引用

页码：1869 / 1891

页数：23

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