Fractional Derivatives and the Fundamental Theorem of Fractional Calculus [PDF]
Fractional Calculus and Applied Analysis, 2020 In this paper, we address the one-parameter families of the fractional integrals and derivatives defined on a finite interval. First we remind the reader of the known fact that under some reasonable conditions, there exists precisely one unique family of the fractional integrals, namely, the well-known Riemann-Liouville fractional integrals.
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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.
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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
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Fractional Calculus Operators and the Mittag-Leffler Function
, 2022 This book focuses on applications of the theory of fractional calculus in numerical analysis and various fields of physics and engineering. Inequalities involving fractional calculus operators containing the Mittag–Leffler function in their kernels are ...
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AN ADAPTIVE MEMORY METHOD FOR ACCURATE AND EFFICIENT COMPUTATION OF THE CAPUTO FRACTIONAL DERIVATIVE
, 2021 A fractional derivative is a temporally nonlocal operation which is com-putationally intensive due to inclusion of the accumulated contribution of function values at past times.
Yoon, Daegeun, You, Donghyun
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Nabla Fractional Derivative and Fractional Integral on Time Scales [PDF]
, 2021 In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann–Liouville sense. We also introduce the nabla fractional derivative in Grünwald–Letnikov sense.
Gogoi, Bikash +9 more
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Fractional variational problems with the Riesz-Caputo derivative
, 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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Fractional variational problems depending on indefinite integrals
, 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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FRACTIONAL CENTRAL DIFFERENCES AND DERIVATIVES [PDF]
IFAC Proceedings Volumes, 2006 Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials.
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An Alternative Definition for the k-Riemann-Liouville Fractional Derivative [PDF]
, 2015 Copyright c © 2014 Gustavo Abel Dorrego. This is an open access article distributed un-der the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly ...
Dorrego, Gustavo +2 more
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