Results 11 to 20 of about 2,052,042 (321)
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 self-adjoint derivative operator.
Berezin F. A. +25 more
core +2 more sources
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
Generalization of Caputo-Fabrizio Fractional Derivative and Applications to Electrical Circuits
Frontiers in Physics, 2020 A new fractional derivative with a non-singular kernel involving exponential and trigonometric functions is proposed in this paper. The suggested fractional operator includes as a special case Caputo-Fabrizio fractional derivative.
Amal Alshabanat +3 more
semanticscholar +3 more sources
No nonlocality. No fractional derivative [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2018 The paper discusses the characteristic properties of fractional derivatives of non-integer order. It is known that derivatives of integer orders are determined by properties of differentiable functions only in an infinitely small neighborhood of the considered point.
Vasily E Tarasov
openaire +4 more sources
A new definition of fractional derivative
Journal of Computational and Applied Mathematics, 2014 Roshdi Khalil +3 more
semanticscholar +3 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 +1 more
openaire +2 more sources
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 +2 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 +1 more
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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 +1 more
doaj +1 more source
A Caputo fractional derivative of a function with respect to another function [PDF]
Communications in nonlinear science & numerical simulation, 2016 In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc.
R. Almeida
semanticscholar +1 more source