Local and global solutions of well-posed integrated Cauchy problems

• Autorzy: Pedro J. Miana
• Języki publikacji: EN

Abstrakty

EN

We study the local well-posed integrated Cauchy problem
$v'(t) = Av(t) + (t^{α})/Γ(α+1)x$, v(0) = 0, t ∈ [0,κ),
with κ > 0, α ≥ 0, and x ∈ X, where X is a Banach space and A a closed operator on X. We extend solutions increasing the regularity in α. The global case (κ = ∞) is also treated in detail. Growth of solutions is given in both cases.

Kategorie tematyczne

• 26A33: Fractional derivatives and integrals
• 47D62: Integrated semigroups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 187
• Numer: 3
• Strony: 219-232

Daty

wydano

2008

Twórcy

autor

Pedro J. Miana

• Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009 Zaragoza, Spain

Identyfikatory

DOI

10.4064/sm187-3-2