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 +5 more
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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
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On Fractional and Fractal Derivatives in Relation to the Physics of Fractals
Recoletos Multidisciplinary Research Journal, 2013 Fractional and fractal derivatives are both generalizations of the usual derivatives that consider derivatives of non-integer orders. Interest in these generalizations has been triggered by a resurgence of clamor to develop a mathematical tool to ...
Roberto N. Padua +6 more
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Comparison principles for fractional differential equations with the Caputo derivatives
Advances in Difference Equations, 2018 In this paper, we deal with comparison principles for fractional differential equations involving the Caputo derivatives of order p with 0≤n ...
Ziqiang Lu, Yuanguo Zhu
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Modelling solute transport in soil columns using advective-dispersive equations with fractional spatial derivatives [PDF]
, 2010 Solute transport in soils is commonly simulated with the advective–dispersive equation, or ADE. It has been reported that this model cannot take into account several important features of solute movement through soil.
San Jose Martinez, Fernando
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Mild and classical solutions to a fractional singular second order evolution problem
Electronic Journal of Qualitative Theory of Differential Equations, 2012 Existence and uniqueness of mild and classical solutions are discussed for an abstract second-order evolution problem. The nonlinearity contains a local term and a non-local term.
Nasser-Eddine Tatar
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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
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Analysis of respiratory mechanics models with different kernels
Open Physics, 2022 In this article, we investigate the mechanics of breathing performed by a ventilator with different kernels by an effective integral transform. We mainly obtain the solutions of the fractional respiratory mechanics model.
Akgül Esra Karatas +6 more
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Solutions of Bernoulli Equations in the Fractional Setting
Fractal and Fractional, 2021 We present a general series representation formula for the local solution of the Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractional logistic equation and present some related numerical simulations.
Mirko D’Ovidio +2 more
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Fractional integration and cointegration in US financial time series data [PDF]
, 2011 This paper examines several US monthly financial time series data using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets ...
Caporale, GM, Gil-Alana, LA
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