A Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval

In this paper, we consider a Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval. An elementary fact shows that semi-infinite interval is not compact, the classical Ascoli-Arzelà theorem is not valid. In order to establish the global existe...

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Bibliographic Details
Published inFractional calculus & applied analysis Vol. 25; no. 3; pp. 924 - 961
Main Authors Zhou, Yong, He, Jia Wei
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2022
Subjects
Abstract Harmonic Analysis
Analysis
Functional Analysis
Integral Transforms
Mathematics
Mathematics and Statistics
Operational Calculus
Original Paper
Semi-infinite interval
Hilfer’s fractional derivative
26A33 (Primary)
34A12
Existence
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Summary:In this paper, we consider a Cauchy problem for fractional evolution equations with Hilfer’s fractional derivative on semi-infinite interval. An elementary fact shows that semi-infinite interval is not compact, the classical Ascoli-Arzelà theorem is not valid. In order to establish the global existence criteria, we first generalize Ascoli-Arzelà theorem into the semi-infinite interval. Next, we introduce a new concept of mild solutions based on cosine/sine family and probability density function and obtain several existence results of mild solutions on semi-infinite interval.
ISSN:1311-0454
1314-2224
DOI:10.1007/s13540-022-00057-9