General fractional calculus

By Anatoly N. Kochubei. Basic Theory, 2019

99 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9a986061ac7ce24f7563a761959bf378c26a0b4d

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Relaxation patterns and semi-Markov dynamics (2015, background): “Kochubei [27] considered operators similar to that appearing in (2.”
A practical guide to Prabhakar fractional calculus (2020, background): “Giusti [42] has then laid down a connection between the so called Prabhakar fractional calculus and Kochubei’s general fractional calculus [87].”
On History of Mathematical Economics: Application of Fractional Calculus (2019, methodology): “Kochubei, the fractional derivatives and integrals of distributed order are investigated in the works [239,240].”
A comment on a controversial issue: A generalized fractional derivative cannot have a regular kernel (2020, background): “The object of our study, which is the relation between the kernels of the generalized fractional derivatives and generalized fractional integral and its implications, is identical in the case of Caputo-type generalized fractional derivatives studied in [13].”
Operational Calculus for the General Fractional Derivative and Its Applications (2021, unknown): “The starting point for involving the general integro-differential operators of convolution type into FC research was the paper [15] (see also [10, 23, 28]).”
Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense (2022, background): “, [7, 8, 9, 11, 12, 13, 14, 21]), to the best of author’s knowledge, only one publication dealing with the fractional differential equations with the GFDs in the Riemann-Liouville sense has been published until now.”
Positivity, monotonicity, and convexity for convolution operators (2020, background): “See a survey in [33] and the papers [27], [21].”
Why fractional derivatives with nonsingular kernels should not be used (2020, methodology): “This analysis is based on ideas previously presented in [6, 11,12,16].”
General Fractional Integrals and Derivatives with the Sonine Kernels (2021, methodology): “The ordinary fractional differential equations with the Caputo type GFDs are addressed in [1,5–7] and the time-fractional diffusion equations with these derivatives are considered in [1,3,5,8–10].”
Fractional derivatives and the fundamental theorem of fractional calculus (2020, background): “These discussions mainly concerned the ”new fractional integrals and derivatives” ( [6, 8, 20, 24–26]), the integro-differential operators of convolution type with some general kernels ( [8, 14, 15, 24, 27, 28]), and the abstract axioms of FC ( [11, 19, 22]).”
Well-posedness of general Caputo-type fractional differential equations (2018, background): “As in [8], we assume that the kernel function k satisfies the following conditions (C1) The Laplace transform k̂ of k, k̂(t) = ∫ ∞”