Results 1 to 10 of about 42,388 (275)
General Fractional Vector Calculus [PDF]
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
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General Fractional Calculus: Multi-Kernel Approach [PDF]
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
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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.
Arran Fernandez, Hafiz Muhammad Fahad
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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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General Fractional Calculus, Evolution Equations, and Renewal Processes [PDF]
Integral Equations and Operator Theory, 2011 We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form $(Du)(t)=\frac{d}{dt}\int\limits_0^tk(t-\tau)u(\tau)\,d\tau -k(t)u(0)$ where $k$ is a nonnegative ...
Kochubei, Anatoly N.
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General Fractional Calculus Operators of Distributed Order
Axioms, 2023 In this paper, two types of general fractional derivatives of distributed order and a corresponding fractional integral of distributed type are defined, and their basic properties are investigated.
Mohammed Al-Refai, Yuri Luchko
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Growth Equation of the General Fractional Calculus [PDF]
Mathematics, 2019 We consider the Cauchy problem ( D ( k ) u ) ( t ) = λ u ( t ) , u ( 0 ) = 1 , where D ( k ) is the general convolutional derivative introduced in the paper (A. N. Kochubei, Integral Equations Oper. Theory 71 (2011),
Anatoly N. Kochubei, Yuri Kondratiev
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Mathematics, 2018 In this note, we show how an initial value problem for a relaxation process governed by a differential equation of a non-integer order with a constant coefficient may be equivalent to that of a differential equation of the first order with a varying ...
Francesco Mainardi
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The Generalized Fractional Calculus of Variations
, 2014 We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods.
Odzijewicz, Tatiana +1 more
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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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