Fractional calculus of periodic distributions [PDF]
, 2011 Two approaches for defining fractional derivatives of periodic distributions are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier
Lamb, Wilson +2 more
core +4 more sources
Unitary fractional-order derivative operators for quantum computation
, 2021 Along with recent progresses in quantum computation technologies, researchers have addressed practical computational supremacies of quantum computers. The research works in the quantum computation domain mainly focus on progressive quantum algorithms and
Alagoz B.B., Alagoz S.
core +1 more source
Fractional variational problems depending on indefinite integrals [PDF]
, 2012 We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral.
Pooseh, Shakoor +8 more
core +1 more source
Fractional variational problems with the Riesz-Caputo derivative [PDF]
, 2012 In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the ...
Almeida, R. +2 more
core +1 more source
Fractional transformations of generalised functions [PDF]
, 2009 A distributional theory of fractional transformations is developed. A constructive approach, based on the eigenfunction expansion method pioneered by A. H.
Lamb, Wilson +2 more
core +4 more sources
Multi-Kernel General Fractional Calculus of Arbitrary Order
, 2023 An extension of the general fractional calculus (GFC) of an arbitrary order, proposed by Luchko, is formulated. This extension is also based on a multi-kernel approach, in which the Laplace convolutions of different Sonin kernels are used.
Vasily E. Tarasov
core +1 more source
Identification of the Order of the Fractional Derivative for the Fractional Wave Equation [PDF]
, 2023 A fractional wave equation with a fractional Riemann–Liouville derivative is considered. An arbitrary self-adjoint operator A with a discrete spectrum was taken as the elliptic part.
Ravshan Ashurov +3 more
core +1 more source
A new general fractional-order derivative with Rabotnov fractional-exponential kernel / [PDF]
, 2019 In this article, a general fractional-order derivative of the Riemann-Liouville type with the non-singular kernel involving the Rabotnov fractional-exponential function is addressed for the first time.
Tana, Thiab, +2 more
core +1 more source
Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme [PDF]
, 2010 A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for ...
Matignon, Denis +3 more
core +1 more source
The Flow Analysis of Fiuids in Fractal Reservoir with the Fractional Derivative
, 2006 In this paper, fractional order derivative, fractal dimension and spectral dimension are introduced into the seepage flow mechanics to establish the flow models of fluids in fractal reservoirs with the fractional derivative.
Tian J +2 more
core +1 more source