Results 21 to 30 of about 11,408,380 (251)

Operational Calculus for the 1st-Level General Fractional Derivatives and Its Applications

Mathematics
The 1st-level General Fractional Derivatives (GFDs) combine in one definition the GFDs of the Riemann–Liouville type and the regularized GFDs (or the GFDs of the Caputo type) that have been recently introduced and actively studied in the fractional ...
Maryam Alkandari, Yuri Luchko
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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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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 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
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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
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Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense

Mathematics, 2022
In this paper, we first consider the general fractional derivatives of arbitrary order defined in the Riemann–Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of fractional calculus ...
Yuri Luchko
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General Fractional Dynamics

Mathematics, 2021
General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional ...
Vasily E. Tarasov
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General Fractional Noether Theorem and Non-Holonomic Action Principle

Mathematics, 2023
Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non ...
Vasily E. Tarasov
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Evaluating an Improper Fractional Integral Based on Jumarie's Modified Riemann-Liouville Fractional Calculus

, 2023
: In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus, we find the solution of some type of improper fractional integral.
Chii-Huei Yu
core   +1 more source

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
doaj   +1 more source