Determination of the order in Abstract fractional differential equations

2023/03/21 by Rodrigo Ponce, Ponce, Rodrigo
Mathematics · #26A33 #34A55 #34K29 #47D06 #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2303.11900

openalex publication_date 2023/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we identify, for small t and a fixed T>0, the order α>0 in the abstract fractional differential equation ∂^αu(t)=Au(t), where the time-fractional derivative ∂^α 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<α<1 or 1<α<2.

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