Generators of Analytic Resolving Families for Distributed Order Equations and Perturbations

被引：10

作者：

Fedorov, Vladimir E. ^{[1
,2
,3
]}

机构：

[1] Chelyabinsk State Univ, Dept Math Anal, Chelyabinsk 454001, Russia

[2] South Ural State Univ, Lab Funct Mat, Chelyabinsk 454080, Russia

[3] Russian Acad Sci, Ural Branch, NN Krasovskii Inst Math & Mech, Dept Differential Equat, Ekaterinburg 620108, Russia

来源：

MATHEMATICS | 2020年 / 8卷 / 08期

基金：

俄罗斯基础研究基金会;

关键词：

distributed order equation; analytic resolving family of operators; generator of resolving family; perturbation theorem; DIFFERENTIATION; CALCULUS;

D O I：

10.3390/math8081306

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Linear differential equations of a distributed order with an unbounded operator in a Banach space are studied in this paper. A theorem on the generation of analytic resolving families of operators for such equations is proved. It makes it possible to study the unique solvability of inhomogeneous equations. A perturbation theorem for the obtained class of generators is proved. The results of the work are illustrated by an example of an initial boundary value problem for the ultraslow diffusion equation with the lower-order terms with respect to the spatial variable.

引用

页数：15

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[Anonymous], 2001, THESIS

[2]

[Anonymous], [No title captured]

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Arendt W, 2011, MG MATH, V96, pIX, DOI 10.1007/978-3-0348-0087-7

[4] On a nonlinear distributed order fractional differential equation [J].