Analysis of Tempered Fractional Calculus in Hölder and Orlicz Spaces

Here, we propose a general framework covering a wide variety of fractional operators. We consider integral and differential operators and their role in tempered fractional calculus and study their analytic properties. We investigate tempered fractional integral operators acting on subspaces of L1[a,...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 8; p. 1581
Main Authors Salem, Hussein A. H., Cichoń, Mieczysław
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2022
Subjects
Banach spaces
Calculus
Differential calculus
Differential equations
Fractional calculus
Hardy–Littlewood theorem
Hölder space
Integral equations
Mathematical analysis
Operators (mathematics)
Orlicz space
Subspaces
tempered fractional calculus
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Summary:Here, we propose a general framework covering a wide variety of fractional operators. We consider integral and differential operators and their role in tempered fractional calculus and study their analytic properties. We investigate tempered fractional integral operators acting on subspaces of L1[a,b], such as Orlicz or Hölder spaces. We prove that in this case, they map Orlicz spaces into (generalized) Hölder spaces. In particular, they map Hölder spaces into the same class of spaces. The obtained results are a generalization of classical results for the Riemann–Liouville fractional operator and constitute the basis for the use of generalized operators in the study of differential and integral equations. However, we will show the non-equivalence differential and integral problems in the spaces under consideration.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14081581