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The Fractional Orthogonal Derivative [PDF]

Mathematics, 2015
This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n.
Enno Diekema
doaj   +3 more sources

Application of Newton’s polynomial interpolation scheme for variable order fractional derivative with power-law kernel [PDF]

Scientific Reports
This paper, offers a new method for simulating variable-order fractional differential operators with numerous types of fractional derivatives, such as the Caputo derivative, the Caputo–Fabrizio derivative, the Atangana–Baleanu fractal and fractional ...
S Naveen, V Parthiban
doaj   +2 more sources

Bilateral Tempered Fractional Derivatives [PDF]

Symmetry, 2021
The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and showed that it cannot be considered as a derivative.
Manuel Duarte Ortigueira, Gabriel Bengochea   +1 more
openaire   +2 more sources

Fractional Derivatives and Projectile Motion

Axioms, 2021
Projectile motion is studied using fractional calculus. Specifically, a newly defined fractional derivative (the Leibniz L-derivative) and its successor (Λ-fractional derivative) are used to describe the motion of the projectile.
Anastasios K. Lazopoulos, Dimitrios Karaoulanis   +1 more
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A new generalized Hilfer-type fractional derivative with applications to space-time diffusion equation

Results in Physics, 2021
This paper is concerned to present and apply a new generalized fractional derivative, that is the Generalized Hilfer-type (GH) fractional derivative.
Tahir Ullah Khan, Muhammad Adil Khan, Yu-Ming Chu   +2 more
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Numerical exploration of thin film flow of MHD pseudo-plastic fluid in fractional space: Utilization of fractional calculus approach

Open Physics, 2021
In this article, thin film flow of non-Newtonian pseudo-plastic fluid is investigated on a vertical wall through homotopy-based scheme along with fractional calculus.
Qayyum Mubashir, Ismail Farnaz, Sohail Muhammad, Imran Naveed, Askar Sameh, Park Choonkil   +5 more
doaj   +1 more source

On Λ-Fractional Viscoelastic Models

Axioms, 2021
Λ-Fractional Derivative (Λ-FD) is a new groundbreaking Fractional Derivative (FD) introduced recently in mechanics. This derivative, along with Λ-Transform (Λ-T), provides a reliable alternative to fractional differential equations’ current solving.
Anastassios K. Lazopoulos, Dimitrios Karaoulanis   +1 more
doaj   +1 more source

Laplace Variational Iteration Method for Modified Fractional Derivatives with Non-singular Kernel [PDF]

Journal of Applied and Computational Mechanics, 2020
A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative ...
Huitzilín Yépez-Martínez, José Francisco Gómez-Aguilar   +1 more
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Differential equations with tempered Ψ-Caputo fractional derivative

Mathematical Modelling and Analysis, 2021
In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative.
Milan Medveď, Eva Brestovanská
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On Fractional Geometry of Curves

Fractal and Fractional, 2021
Fractional Differential Geometry of curves is discussed, with the help of a new fractional derivative, the Λ-fractional derivative, with the corresponding Λ-fractional space.
Konstantinos A. Lazopoulos, Anastasios K. Lazopoulos   +1 more
doaj   +1 more source