On generalized fractional operators and related function spaces with applications

The application of fractional calculus-based mathematical models in physics is a well-established practice. However, a challenge arises due to the variety of fractional operators used in these models and the search for solutions in different function spaces. This paper proposes a unified approach to...

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Bibliographic Details
Published in:Physica. D Vol. 465; p. 134212
Main Authors: Cichoń, Kinga, Cichoń, Mieczysław
Format: Journal Article
Language:English
Published: Elsevier B.V 01.09.2024
Subjects:
Bounded variation
Fractional integral operators
Hölder spaces
Modulus of continuity
Subdiffusion
Fractional integral operators
Bounded variation
Modulus of continuity
Hölder spaces
Subdiffusion
ISSN:0167-2789, 1872-8022
Online Access:Get full text
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Summary:The application of fractional calculus-based mathematical models in physics is a well-established practice. However, a challenge arises due to the variety of fractional operators used in these models and the search for solutions in different function spaces. This paper proposes a unified approach to this issue by applying general fractional operators that can capture and extend previous attempts, with appropriate parameters that align with the features of the phenomena being modeled. The main goal is to establish invariant spaces for these operators. This will simplify the application of various proof techniques. •Fractional problems with a parametrized definition of fractional integral operators.•An appropriate invariant domain for this class of operators is constructed.•A general class of fractional-order operators used to model nonlinear phenomena.•The invariance of the operator on the proposed space is demonstrated.•The method is applicable to differential problems with data of non-polynomial growth.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2024.134212