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Thermodynamics in Fractional Calculus
Journal of Engineering Physics and Thermophysics, 2014A generalization of thermodynamics in the formalism of fractional-order derivatives is given. Results of the traditional thermodynamics of Carnot, Clausius, and Helmholtz are obtained in the particular case where the exponent of a fractional-order derivative is equal to unity. A one-parametric "fractal" equation of state is obtained with account of the
R. A. Magomedov, R. P. Meilanov
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Fractional Calculus in Bioengineering, Part3
Critical Reviews in Biomedical Engineering, 2004Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the ...
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Essentials of Fractional Calculus
2017In recent decades, the field of fractional calculus has attracted interest of researchers in several areas including mathematics, physics, chemistry, engineering, and even finance and social sciences.
Hans J. Haubold, Arak M. Mathai
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Chaos, Solitons & Fractals, 2009
Abstract Here are presented fractional Taylor type formulae with fractional integral remainder and fractional differential formulae, regarding the right Caputo fractional derivative, the right generalized fractional derivative of Canavati type [Canavati JA. The Riemann–Liouville integral.
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Abstract Here are presented fractional Taylor type formulae with fractional integral remainder and fractional differential formulae, regarding the right Caputo fractional derivative, the right generalized fractional derivative of Canavati type [Canavati JA. The Riemann–Liouville integral.
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2015
As mentioned in the previous chapter and as demonstrated on numerous occasions, the disadvantage of the discrete delta fractional calculus is the shifting of domains when one goes from the domain of the function to the domain of its delta fractional difference. This problem is not as great with the fractional nabla difference as noted by Atici and Eloe.
Allan Peterson, Christopher S. Goodrich
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As mentioned in the previous chapter and as demonstrated on numerous occasions, the disadvantage of the discrete delta fractional calculus is the shifting of domains when one goes from the domain of the function to the domain of its delta fractional difference. This problem is not as great with the fractional nabla difference as noted by Atici and Eloe.
Allan Peterson, Christopher S. Goodrich
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The Fractional Calculus of Variations
2018In this chapter, we consider general fractional problems of the calculus of variations, where the Lagrangian depends on a combined Caputo fractional derivative of variable fractional order \(^CD_\gamma ^{{\alpha (\cdot ,\cdot )},{\beta (\cdot ,\cdot )}}\) given as a combination of the left and the right Caputo fractional derivatives of orders ...
Ricardo Almeida +2 more
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An introduction to fractional calculus
2009An introduction to fractional ...
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, 2018 Beyond food: The multiple pathways for inclusion of materials into ancient dental calculus
American Journal of Physical Anthropology, 2017Anita Radini +2 more
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