Existence of solutions of the abstract Cauchy problem of fractional order

Hernán R Henríquez,Jaqueline G Mesquita,Juan C Pozo

doi:10.1016/j.jfa.2021.109028

Existence of solutions of the abstract Cauchy problem of fractional order

Hernán R Henríquez, Jaqueline G Mesquita + Show 1 more

https://doi.org/10.1016/j.jfa.2021.109028

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Journal: Journal of Functional Analysis	Publication Date: Apr 7, 2021
Citations: 11

Affiliation: University of Chile, Universidade de Brasília, University of Santiago Chile

#Cauchy Problem #Solutions For Cauchy Problem + Show 8 more

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Abstract

In this paper, we study the differentiability of mild solutions for a class of fractional abstract Cauchy problem. We consider the fractional derivative of order α∈(1,2) in the sense of Caputo. In the first part, we establish the existence of classical solutions for the homogeneous Cauchy problem in terms of the α-resolvent family corresponding to the problem and, in the second part, we establish the existence of classical solutions for the inhomogeneous abstract Cauchy problem in terms of regularity properties of the α-resolvent family and of the forcing function.

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