Results 1 to 10 of about 1,816,969 (371)

Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus. [PDF]

Entropy (Basel), 2023
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry.
Deppman A, Megías E, Pasechnik R.
europepmc   +3 more sources

Combining Fractional Derivatives and Machine Learning: A Review. [PDF]

Entropy (Basel), 2022
Fractional calculus has gained a lot of attention in the last couple of years. Researchers have discovered that processes in various fields follow fractional dynamics rather than ordinary integer-ordered dynamics, meaning that the corresponding ...
Raubitzek S, Mallinger K, Neubauer T.
europepmc   +2 more sources

A delayed plant disease model with Caputo fractional derivatives. [PDF]

Adv Contin Discret Model, 2022
We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington–DeAngelis functional response to study the structure of a vector-borne plant epidemic.
Kumar P, Baleanu D, Erturk VS, Inc M, Govindaraj V.   +4 more
europepmc   +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   +2 more sources

FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE [PDF]

International Journal of Mathematics, 2007
Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator.
Berezin F. A., Berezin F. A., Brichkov Yu. A., Caputo M., Dalechky Yu. L., Hadid S. B., Karasev M. V., Korabel N., Krasnolelsky M. A., Krasnolelsky M. A., Krein S. G., Krein S. G., Le Mehaute A., Luke Y., Maslov V. P., Momani S., Oldham K. B., Samko S. G., Tarasov V. E., Tarasov V. E., Tarasov V. E., Tarasov V. E., Tarasov V. E., Tarasov V. E., VASILY E. TARASOV, Zaslavsky G. M.   +25 more
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Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense [PDF]

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
doaj   +2 more sources

Operational Calculus for the General Fractional Derivatives of Arbitrary Order

Mathematics, 2022
In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin.
Maryam Al-Kandari, Latif A-M. Hanna, Yuri Luchko   +2 more
doaj   +2 more sources

Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan. [PDF]

Eur Phys J Plus, 2020
Coronaviruses are a large family of viruses that cause different symptoms, from mild cold to severe respiratory distress, and they can be seen in different types of animals such as camels, cattle, cats and bats.
Naik PA, Yavuz M, Qureshi S, Zu J, Townley S.   +4 more
europepmc   +2 more sources

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

Hilfer–Katugampola fractional derivatives

Computational and Applied Mathematics, 2017
We propose a new fractional derivative, the Hilfer-Katugampola fractional derivative. Motivated by the Hilfer derivative this formulation interpolates the well-known fractional derivatives of Hilfer, Hilfer-Hadamard, Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, Liouville, Weyl, generalized and Caputo-type.
Oliveira, D. S., de Oliveira, E. Capelas
openaire   +3 more sources