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On a Generalized Class of Non-Singular Kernel Operators and Their Singular Kernel Extensions: Useful Modeling Insights
- Source :
- Journal of Computational and Nonlinear Dynamics; 20240101, Issue: Preprints p1-16, 16p
- Publication Year :
- 2024
-
Abstract
- Some possible definitions of fractional derivative operators with non-singular analytic kernels have been introduced. In this paper, we propose a new generalized class of fractional derivative operators of Caputo-type with non-singular analytic kernels which includes some known operators as special cases. We demonstrate a relationship between the fractional derivative operators of the proposed generalized class and the Riemann-Liouville fractional integral operator. We also, using this relationship, introduce the corresponding fractional integral operators. Then, mainly, we provide extensions to the fractional derivative operators of the proposed generalized class that display integrable singular kernels. The extended fractional derivative operators provide useful insights regarding the modeling issue so that the initialization problem can be overcome. Finally, we discuss some basic properties of the proposed operators that are expected to be widely used in fractional calculus.
Details
- Language :
- English
- ISSN :
- 15551415 and 15551423
- Issue :
- Preprints
- Database :
- Supplemental Index
- Journal :
- Journal of Computational and Nonlinear Dynamics
- Publication Type :
- Periodical
- Accession number :
- ejs67430884
- Full Text :
- https://doi.org/10.1115/1.4066571