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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
exaly   +5 more sources

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 Fernández
exaly   +5 more sources

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
exaly   +5 more sources

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
doaj   +3 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
doaj   +1 more source

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   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

General Nonlocal Probability of Arbitrary Order

Entropy, 2023
Using the Luchko’s general fractional calculus (GFC) and its extension in the form of the multi-kernel general fractional calculus of arbitrary order (GFC of AO), a nonlocal generalization of probability is suggested. The nonlocal and general fractional (
Vasily E. Tarasov
doaj   +1 more source

The General Fractional Integrals and Derivatives on a Finite Interval

Mathematics, 2023
The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for the functions on the real positive semi-axis.
Mohammed Al-Refai, Yuri Luchko
doaj   +1 more source