THERMAL SCIENCE

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Xiao-Jun Yang

NEW NON-CONVENTIONAL METHODS FOR QUANTITATIVE CONCEPTS OF ANOMALOUS RHEOLOGY

ABSTRACT
This paper addresses the general calculus operators with respect to another functions containg the power-law and exponential functions. The Boltzmann-type superposition principles for the anomalous linear viscoelasticity are considered for the first time. The new technologies are as non-conventional tools proposed to extend the quantitative concepts of anomalous rheology for solid mechanics.
KEYWORDS
heat transfer, fractional derivative of constant, fractional derivative of variable order, fractional differential equation, anomalous relaxation
PAPER SUBMITTED: 2019-11-03
PAPER REVISED: 2019-11-04
PAPER ACCEPTED: 2019-11-04
PUBLISHED ONLINE: 2019-11-17
DOI REFERENCE: https://doi.org/10.2298/TSCI191028427Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 6, PAGES [4117 - 4127]
REFERENCES
  1. Newton, I. S. Method of Fluxions, 1665
  2. Leibniz, G. W., Nova Methodus pro Maximis et Minimis, Itemque Tangentibus, qua nec Irrationals Quantitates Moratur. Acta Eruditorum, 1684
  3. Yang, X. J., New General Calculi with Respect to Another Functions Applied to Describe the Newton-like Dashpot Models in Anomalous Viscoelasticity, Thermal Science, 2019, DOI: TSCI180921260Y
  4. Yang, X. J., Gao, F., Ju, Y. (2020). General Fractional Derivatives with Applications in Viscoelasticity, Academic Press, New York, 2012
  5. Yang, X. J., Gao, F., Jing. H. W., New Mathematical Models in Anomalous Viscoelasticity from the Derivative with Respect to Another Function View Point, Thermal Science, 23(2019), 3A, pp.1555-1561
  6. Boltzmann, L., Zur Theorie der Elastischen Nachwirkung, Annalen der Physik, 241(1878),11, pp.430-432
  7. Mainardi, F., Fractional Calculus and Waves in Linear Viscoelasticity: an Introduction to Mathematical Models,World Scientific, Singapore, 2010
  8. Rabotnov, Y., Equilibrium of an Elastic Medium with After-Effect, Prikladnaya Matematika i Mekhanika, 12 (1948), 1, pp. 53-62 (in Russian), Reprinted: Fractional Calculus and Applied Analysis, 17 (2014), 3, pp. 684-696
  9. Rabani, E., Gezelter, J. D., Berne, B. J., Direct Observation of Stretched-exponential Relaxation in Low-temperature Lennard-Jones Systems Using the Cage Correlation Function, Physical Review Letters, 82(1999), 18, pp.3649
  10. West, G. B., Brown, J. H., Enquist, B. J., The Fourth Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms, Science, 284(1999), 5420, pp.1677-1679
  11. Larson, R., Edwards, B., Calculus, Eleventh Edition, Cengage Learning, United States, 2016
  12. Kohlrausch, R., Theorie des elektrischen Rückstandes in der Leidener Flasche, Annalen der Physik, 167(1854), 2, pp.179-214
  13. Williams, G., Watts, D. C., Non-symmetrical Dielectric Relaxation Behaviour Arising from a Simple Empirical Decay Function, Transactions of the Faraday Society, 66(1970), June, pp.80-85
  14. Shlesinger, M. F., Montroll, E. W., On the Williams—Watts Function of Dielectric Relaxation, Proceedings of the National Academy of Sciences, 81(1984), 4, pp.1280-1283
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New non-conventional methods for quantitative concepts of anomalous rheology

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, 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