Theory on New Fractional Operators Using Normalization and Probability Tools Article Swipe
We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel class of linear operators with memory effects to extend the L-fractional and the ordinary derivatives, using probability tools. A Mittag–Leffler-type function is introduced to solve linear problems, and nonlinear equations are addressed with power series, illustrating the methods for the SIR epidemic model. The inverse operator is constructed, and a fundamental theorem of calculus and an existence-and-uniqueness result for differintegral equations are proven. A conjecture on deconvolution is raised, which would permit completing the proposed theory.
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Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/fractalfract8110665
- OA Status
- gold
- Cited By
- 13
- References
- 44
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4404415219
All OpenAlex metadata
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https://openalex.org/W4404415219Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3390/fractalfract8110665Digital Object Identifier
- Title
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Theory on New Fractional Operators Using Normalization and Probability ToolsWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
-
2024-11-15Full publication date if available
- Authors
-
Marc JornetList of authors in order
- Landing page
-
https://doi.org/10.3390/fractalfract8110665Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
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https://doi.org/10.3390/fractalfract8110665Direct OA link when available
- Concepts
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Normalization (sociology), Mathematics, Computer science, Applied mathematics, Sociology, AnthropologyTop concepts (fields/topics) attached by OpenAlex
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13Total citation count in OpenAlex
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2025: 9, 2024: 4Per-year citation counts (last 5 years)
- References (count)
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44Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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