Representation of Fractional Operators Using the Theory of Functional Connections
Mathematics, 2023 This work considers fractional operators (derivatives and integrals) as surfaces f(x,α) subject to the function constraints defined by integer operators, which is a mandatory requirement of any fractional operator definition. In this respect, the problem
Daniele Mortari
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Some fractional proportional integral inequalities
Journal of Inequalities and Applications, 2019 In the last few years, various researchers studied the so-called conformable integrals and derivatives. Based on that notion some authors used modified conformable derivatives (proportional derivatives) to generate nonlocal fractional integrals and ...
Gauhar Rahman +3 more
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Fractional boundary value problems: Analysis and numerical methods [PDF]
, 2011 This is the author's PDF of an article published in Fractional Calculus and Applied Analysis 2011. The original publication is available at www.springerlink.comThis journal article discusses nonlinear boundary value problems.Fundacao para a Ciencia e ...
M. Luísa Morgado +3 more
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Positive Solutions of a Singular Fractional Boundary Value Problem with r-Laplacian Operators
Fractal and Fractional, 2021 We investigate the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations with r-Laplacian operators and nonnegative singular nonlinearities depending on fractional integrals, supplemented ...
Alexandru Tudorache, Rodica Luca
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General Fractional Calculus: Multi-Kernel Approach
Mathematics, 2021 For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
Vasily E. Tarasov
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Diffusive representations for fractional Laplacian: systems theory framework and numerical issues [PDF]
, 2009 Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not ...
Matignon, Denis
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Input-output linearization and fractional robust control of a non-linear system [PDF]
, 2001 This article deals with the association of a linear robust controller and an input-output linearization feedback for the control of a perturbed and non-linear system.
Oustaloup, Alain +7 more
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E. R. LOVE TYPE LEFT FRACTIONAL INTEGRAL INEQUALITIES
Проблемы анализа, 2020 Here first we derive a general reverse Minkowski integral inequality. Then motivated by the work of E. R. Love [4] on integral inequalities we produce general reverse and direct integral inequalities.
G. A. Anastassiou
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On a discrete composition of the fractional integral and Caputo derivative [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2022 This is an accepted version of the manuscript published in Communications in Nonlinear Science and Numerical Simulations. The changes with the previous versions included some language corrections, additional numerical simulations, and new ...
openaire +2 more sources
Partial, Composite Fractional Operators, and Their Properties and Applications
MATEC Web of Conferences, 2017 The paper discusses the properties of the partial fractional integrals, the partial fractional derivatives, and the composite fractional integrals and derivatives.
Deng Kaiying, Deng Jingwei, Li Suduo
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