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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| Vydáno v: | Physica. D Ročník 465; s. 134212 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
01.09.2024
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| Témata: | |
| ISSN: | 0167-2789, 1872-8022 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
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| ISSN: | 0167-2789 1872-8022 |
| DOI: | 10.1016/j.physd.2024.134212 |