General Fractional Integrals and Derivatives with the Sonine Kernels
By Yuri Luchko. Mathematics, 2021
141 citations recorded by the source corpus.
In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero. First, the Sonine kernels and their important special classes and particular cases are discussed. In particular, we introduce a class of the Sonine kernels that possess an integrable singularity of power function type at the point zero. For the general fractional integrals and derivatives with the Sonine kernels from this class, two fundamental theorems of fractional calculus are proved. Then, we construct the n-fold general fractional integrals and derivatives and study their properties.
Subfields: Geometry and Topology, Modeling and Simulation, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a58113973e7cfceabbe8d04837d69dfa4d3492b1
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Citations in the corpus
- Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense (2022, methodology): “In [18], these operators were studied on the space of functions continuous on the real positive semi-axis that can have an integrable singularity of power function type at the point zero.”