Results 11 to 20 of about 34,631 (216)

Fractional Derivatives Application to Image Fusion Problems [PDF]

Sensors, 2022
In this paper, an analysis of the method that uses a fractional order calculus to multispectral images fusion is presented. We analyze some correct basic definitions of the fractional order derivatives that are used in the image processing context ...
Szymon Motłoch, Grzegorz Sarwas, Andrzej Dzieliński   +2 more
doaj   +2 more sources

How Many Fractional Derivatives Are There?

Mathematics, 2022
In this paper, we introduce a unified fractional derivative, defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained.
Duarte Valério, Manuel D. Ortigueira, António M. Lopes   +2 more
doaj   +3 more sources

The mathematical description of the bulk fluid flow and that of the content impurity dispersion, obtained by replacing integer order temporal derivatives with general temporal Caputo or general temporal Riemann-Liouville fractional order derivatives, are objective [PDF]

INCAS Bulletin, 2021
In the field of fractional calculus applications, there is a tendency to admit that “integer-order derivatives cannot simply be replaced by fractional-order derivatives to develop fractional-order theories”.
Agneta M. BALINT, Stefan BALINT
doaj   +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
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On the 1st-Level General Fractional Derivatives of Arbitrary Order

Fractal and Fractional, 2023
In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and ...
Yuri Luchko
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

On Λ-Fractional Analysis and Mechanics

Axioms, 2022
Λ-Fractional analysis was introduced to fill up the mathematical gap exhibited in fractional calculus, where the various fractional derivatives fail to fulfill the prerequisites demanded by differential topology.
Konstantinos A. Lazopoulos
doaj   +1 more source

On the fractional deformation of a linearly elastic bar

Journal of the Mechanical Behavior of Materials, 2020
Fractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local ...
Lazopoulos Konstantinos A., Lazopoulos Anastasios K.   +1 more
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Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations

Journal of Advanced Research, 2023
Introduction: Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement ...
Mohammad Hossein Heydari, Mohsen Razzaghi, Dumitru Baleanu   +2 more
doaj   +1 more source

Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics, 2021
In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator.
Fátima Cruz, Ricardo Almeida, Natália Martins   +2 more
doaj   +1 more source