Results 11 to 20 of about 42,388 (275)
General Fractional Calculus in Multi-Dimensional Space: Riesz Form
Mathematics, 2023 An extension of the general fractional calculus (GFC) is proposed as a generalization of the Riesz fractional calculus, which was suggested by Marsel Riesz in 1949.
Vasily E. Tarasov
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Scale-Invariant General Fractional Calculus: Mellin Convolution Operators
Fractal and Fractional, 2023 General fractional calculus (GFC) of operators that is defined through the Mellin convolution instead of Laplace convolution is proposed. This calculus of Mellin convolution operators can be considered as an analogue of the Luchko GFC for the Laplace ...
Vasily E. Tarasov
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General fractional calculus and Prabhakar’s theory [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2020 General fractional calculus offers an elegant and self-consistent path toward the generalization of fractional calculus to an enhanced class of kernels. Prabhakar's theory can be thought of, to some extent, as an explicit realization of this scheme achieved by merging the Prabhakar (or, three-parameter Mittag-Leffler) function with the general wisdom ...
Andrea Giusti
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Multi-Kernel General Fractional Calculus of Arbitrary Order
Mathematics, 2023 An extension of the general fractional calculus (GFC) of an arbitrary order, proposed by Luchko, is formulated. This extension is also based on a multi-kernel approach, in which the Laplace convolutions of different Sonin kernels are used.
Vasily E. Tarasov
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Zener Model with General Fractional Calculus: Thermodynamical Restrictions
Fractal and Fractional, 2022 We studied a Zener-type model of a viscoelastic body within the context of general fractional calculus and derived restrictions on coefficients that follow from the dissipation inequality, which is the entropy inequality under isothermal conditions.
Teodor M. Atanackovic, Stevan Pilipovic
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Operational Calculus for the General Fractional Derivatives of Arbitrary Order
Mathematics, 2022 In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin.
Maryam Al-Kandari +2 more
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On fractional calculus with general analytic kernels [PDF]
Applied Mathematics and Computation, 2019 Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions.
Arran Fernandez +2 more
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Generalized Fractional Calculus for Gompertz-Type Models [PDF]
Mathematics, 2021 This paper focuses on the construction of deterministic and stochastic extensions of the Gompertz curve by means of generalized fractional derivatives induced by complete Bernstein functions. Precisely, we first introduce a class of linear stochastic equations involving a generalized fractional integral and we study the properties of its solutions ...
Giacomo Ascione, Enrica Pirozzi
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Haar wavelet fractional derivative [PDF]
Proceedings of the Estonian Academy of Sciences, 2022 In this paper, the fundamental properties of fractional calculus are discussed with the aim of extending the definition of fractional operators by using wavelets.
Carlo Cattani
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General Non-Local Continuum Mechanics: Derivation of Balance Equations
Mathematics, 2022 In this paper, mechanics of continuum with general form of nonlocality in space and time is considered. Some basic concepts of nonlocal continuum mechanics are discussed. General fractional calculus (GFC) and general fractional vector calculus (GFVC) are
Vasily E. Tarasov
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