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Two compartmental fractional derivative model with general fractional derivative
Journal of Pharmacokinetics and Pharmacodynamics, 2022This study presents a new two compartmental model with, recently defined General fractional derivative. We review that concept of General fractional derivative and use the kernel function that generalizes the classical Caputo derivative in a mathematically consistent way.
Vesna Miskovic-Stankovic +2 more
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What is a fractional derivative?
Journal of Computational Physics, 2015This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grunwald-Letnikov, Riemann-Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the ...
Ortigueira, Manuel +1 more
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Heparin Fractions and Derivatives
Seminars in Thrombosis and Hemostasis, 1985Thromboembolic disease continues to plague mankind because it is often detected too late for effective management, because modern therapeutic measures are often inefficiently managed, and because new therapeutic agents and available laboratory tests are ignored.
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Fractional Derivative and Fractional Integral
2018For every α > 0 and a local integrable function f(t), the right FI of order α is defined: $$\displaystyle{ }_aI_t^\alpha f(t) = \displaystyle\frac {1}{\Gamma (\alpha )}\displaystyle\int _a^t(t - u)^{\alpha - 1}f(u)du,\qquad-\infty \le a < t < \infty .$$
J. A. Tenreiro Machado +2 more
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Two compartmental fractional derivative model with fractional derivatives of different order
Communications in Nonlinear Science and Numerical Simulation, 2013Abstract This study presents a new two compartmental model that contains fractional derivatives of different order. The model is so formulated that the mass balance is preserved. In this way we give an answer on a claim that such a model is not possible.
Popovic, Jovan +2 more
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Remarks on fractional derivatives
Applied Mathematics and Computation, 2007In this paper, we further discuss the properties of three kinds of fractional derivatives: the Grunwald-Letnikov derivative, the Riemann-Liouville derivative and the Caputo derivative. Especially, we compare the Riemann-Liouville derivative with the Caputo derivative. And sequential property of the Caputo derivative is also derived, which is helpful in
Weihua Deng, Changpin Li
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Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2003
A new definition of fractional order derivative is given and its basic properties are investigated. This definition is based on the Weyl derivative and is a local property of functions. It can be applied to non-differentiable functions and may be useful for studying fractal curves.
Matt Davison +2 more
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A new definition of fractional order derivative is given and its basic properties are investigated. This definition is based on the Weyl derivative and is a local property of functions. It can be applied to non-differentiable functions and may be useful for studying fractal curves.
Matt Davison +2 more
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On a Unified Fractional Derivative
Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B, 2011A new fractional derivative of complex Gru¨wald-Letnikov type is proposed and some properties are studied. The new definition incorporates both the forward and backward Gru¨wald-Letnikov and other fractional derivatives well known. Several properties of such generalized operator are presented.
Manuel Duarte Ortigueira +1 more
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Mechanics with fractional derivatives
Physical Review E, 1997Lagrangian and Hamiltonian mechanics can be formulated to include derivatives of fractional order [F. Riewe, Phys. Rev. 53, 1890 (1996)]. Lagrangians with fractional derivatives lead directly to equations of motion with nonconservative classical forces such as friction.
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