Determination of the order in Abstract fractional differential equations

Rodrigo Ponce

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arXiv · 2303.11900

Determination of the order in Abstract fractional differential equations

Rodrigo Ponce

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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 $1<\alpha<2.$

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Rodrigo Ponce. 2023-03-21. Determination of the order in Abstract fractional differential equations. https://arxiv.org/abs/2303.11900

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