Unstable manifolds for fractional differential equations

Research output: Contribution to journal › Research article › Contributed › peer-review

Contributors

  • S. Piskarev - , Lomonosov Moscow State University (Author)
  • S. Siegmund - , Chair of Dynamics and Control, TUD Dresden University of Technology (Author)

Abstract

We prove the existence of unstable manifolds for an abstract semilinear fractional differential equation Dαu(t) = Au(t) + f(u(t)); u(0) = u0; on a Banach space. We then develop a general approach to establish a semidiscrete approximation of unstable manifolds. The main assumption of our results are naturally satisfied.

Details

Original languageEnglish
Pages (from-to)58-72
Number of pages15
JournalEurasian Journal of Mathematical and Computer Applications
Volume10
Issue number3
Publication statusPublished - 2022
Peer-reviewedYes

External IDs

ORCID /0000-0003-0967-6747/work/172084901

Keywords

ASJC Scopus subject areas

Keywords

  • Abstract differential equations, Analytic c -semigroups, Banach spaces, Compact convergence of resolvents, Discretization in space, Fractional differential equations, Fractional powers of operators, Hyperbolic equilibrium point, Parabolic problem, Semidiscretization, Unstable manifolds