Results 11 to 20 of about 11,408,380 (251)
Weighted Fractional Calculus: A General Class of Operators
Fractal and Fractional, 2022 We conduct a formal study of a particular class of fractional operators, namely weighted fractional calculus, and its extension to the more general class known as weighted fractional calculus with respect to functions.
Hafiz Muhammad Fahad, Arran Fernandez
exaly +4 more sources
General Fractional Vector Calculus
Mathematics, 2021 A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators.
Vasily E. Tarasov
exaly +4 more sources
General Fractional Calculus: Multi-Kernel Approach
Mathematics, 2021 For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
Vasily E. Tarasov
exaly +4 more sources
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
doaj +2 more sources
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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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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Nonlocal Probability Theory: General Fractional Calculus Approach
Mathematics, 2022 Nonlocal generalization of the standard (classical) probability theory of a continuous distribution on a positive semi-axis is proposed. An approach to the formulation of a nonlocal generalization of the standard probability theory based on the use of ...
Vasily E. Tarasov
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Semi-integration of certain algebraic expressions [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 The theory of fractional calculus developed rapidly as the applications of this branch are extensive nowadays. There is no discipline of modern engineering and science that remains untouched by the techniques of fractional calculus. In fact, one
M.I. Qureshi, J. Majid
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Fractional calculus of periodic distributions [PDF]
, 2011 Two approaches for defining fractional derivatives of periodic distributions are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier
Lamb, Wilson +5 more
core +4 more sources