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FRACTIONAL MAXWELL FLUID WITH FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL

ABSTRACT
In this paper we propose a new model for the fractional Maxwell fluid within fractional Caputo-Fabrizio derivative operator. We present the fractional Maxwell fluid in the differential form for the first time. The analytical results for the proposed model with the fractional Losada-Nieto integral operator are given to illustrate the efficiency of the fractional order operators to the line viscoelasticity.
KEYWORDS
PAPER SUBMITTED: 2015-12-01
PAPER REVISED: 2016-01-18
PAPER ACCEPTED: 2016-02-23
PUBLISHED ONLINE: 2016-09-24
DOI REFERENCE: https://doi.org/10.2298/TSCI16S3871G
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S871 - S877]
REFERENCES
  1. Blair, G. S., The Role of Psychophysics in Rheology, Journal of Colloid Science, 2 (1947), 1, pp. 21-32
  2. Debnath, L., Recent Applications of Fractional Calculus to Science and Engineering, International Journal of Mathematics and Mathematical Sciences, 2003 (2003), 54, pp. 3413-3442
  3. Rogosin, S., Mainardi, F., George William Scott Blair - the Pioneer of Fractional Calculus in Rheology, Communications in Applied and Industrial Mathematics, 6 (2014), 1, e681
  4. Gerasimov, A. N., A Generalization of Linear Laws of Deformation and Its Application to Problems of Internal Friction (in Russian), Akad. Nauk SSSR. Prikl. Mat. Meh., 12 (1948), pp. 251-260
  5. Kai-Xin, H., et al., Mechanical Analogies of Fractional Elements, Chinese Physics Letters, 26 (2009), 10, ID 108301
  6. Caputo, M., Mainardi, F., Linear Models of Dissipation in Anelastic Solids, Rivista del Nuovo Cimento (Ser. II), 1 (1971), 2, pp. 161-198
  7. Mainardi, F., An Historical Perspective on Fractional Calculus in Linear Viscoelasticity, Fractional Calculus and Applied Analysis, 15 (2012), 4, pp. 712-717
  8. Carpinteri, A., Mainardi, F., Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, New York, USA, 1997
  9. Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier Science Limited, Amsterdam, The Netherlands, 2006
  10. Yang, X.-J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
  11. Caputo, M., Fabrizio, M., A New Definition of Fractional Derivative without Singular Kernel, Progress in Fractional Differentiation and Applications, 1 (2015), 2, pp. 73-85
  12. Lozada, J., Nieto, J. J. Properties of a New Fractional Derivative without Singular Kernel, Progress in Fractional Differentiation and Applications, 1 (2015), 2, pp. 87-92
  13. Alsaedi, A., et al., Fractional Electrical Circuits, Advances in Mechanical Engineering, 7 (2015), 12, pp. 1-7
  14. Atangana, A., Nieto, J. J., Numerical Solution for the Model of RLC Circuit via the Fractional Derivative without Singular Kernel, Advances in Mechanical Engineering, 7 (2015), 10, pp. 1-7
  15. Gomez-Aguilar, J. F., et al., Modeling of a Mass-Spring-Damper System by Fractional Derivatives with and without a Singular Kernel, Entropy, 17 (2015), 9, pp. 6289-6303
  16. Mainardi, F., Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, World Scientific, Singapore, 2010

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence