Determination of the order in Abstract fractional differential equations

Rodrigo Ponce

Determination of the order in Abstract fractional differential equations

Functional Analysis 2023-03-22 v1

Authors: Rodrigo Ponce

Abstract

In this paper we identify, for small $t$ and a fixed $T>0,$ the order $\alpha>0$ in the abstract fractional differential equation $\partial^\alpha u(t)=Au(t),$ where the time-fractional derivative $\partial^\alpha$ is understood in the sense of Caputo and Riemann-Liouville, $A$ is a closed (possibly unbounded) linear operator in a Banach space $X,$ and $0<\alpha<1$ or $1<\alpha<2.$

Keywords

abstract fractional differential equation order identification caputo derivative riemann-liouville derivative banach space closed linear operator

Cite

@article{arxiv.2303.11900,
  title  = {Determination of the order in Abstract fractional differential equations},
  author = {Rodrigo Ponce},
  journal= {arXiv preprint arXiv:2303.11900},
  year   = {2023}
}

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