Dissipativity and stability for a nonlinear differential equation with distributed order symmetrized fractional derivative
- Atanacković, Teodor M.
- Dolićanin, Diana
- Konjik, Sanja
- Pilipović, Stevan
Publication date
June 2011
DOI Publisher
Elsevier Ltd. ISSN
0893-9659 Citation count (estimate)
4Abstract
AbstractWe study the solvability, dissipativity and stability for the equation d2dt2u(t)+b∫01±ETαu(t)ϕ(α)dα+F(u(t))=0,t∈[0,T],T>0, where ∫01±ETαu(t)ϕ(α)dα is the distributed order symmetrized Caputo fractional derivative of u, ϕ(α),α∈(0,1), is a positive integrable function or a distribution of the form ∑i=0ncαiδ(α−αi), 0≤α0<α1<⋯<αn≤1, cαi≥0, i=0,1,…,n, and F(u), u∈R, is a locally Lipschitz continuous function on R
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