Dissipativity and stability for a nonlinear differential equation with distributed order symmetrized fractional derivative

被引：5

作者：

Atanackovic, Teodor M. ^{[1
]}

Dolicanin, Diana ^{[2
]}

Konjik, Sanja ^{[1
]}

Pilipovic, Stevan ^{[1
]}

机构：

[1] Univ Novi Sad, Novi Sad 21000, Serbia

[2] Univ Pristina, Pristina, Serbia

来源：

APPLIED MATHEMATICS LETTERS | 2011年 / 24卷 / 06期

关键词：

Fractional derivatives; Distributions; Dissipation inequality; Stability of solutions;

D O I：

10.1016/j.aml.2011.01.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the solvability, dissipativity and stability for the equation d(2)/dt(2) u (t) + b integral(1)(0) +/- epsilon(alpha)(T)u(t)phi(alpha) d alpha + F(u(t)) = 0. t is an element of vertical bar 0, T vertical bar. T > 0. where integral(1)(0) +/- epsilon(alpha)(T)u(t)phi(alpha) d alpha is the distributed order symmetrized Caputo fractional derivative of u, phi(alpha), alpha is an element of (0, 1), is a positive integrable function or a distribution of the form Sigma(n)(i=0) c(alpha) delta(alpha-alpha(i)), 0 <= alpha(0) < alpha(1) < ... < alpha(n) <= 1, c(alpha i) >= 0, i = 0.1, .... n, and F(u), u is an element of R, is a locally Lipschitz continuous function on R. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1020 / 1025

页数：6

共 15 条

[1] Calculus of variations with fractional derivatives and fractional integrals [J].