THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

AN ANALYTICAL SOLUTION FOR SOLVING A NEW GENERAL FRACTIONAL-ORDER MODEL FOR WAVE IN MINING ROCK

ABSTRACT
In this paper, we consider the general fractional-order derivatives of the Liouville-Sonine-Caputo and Liouville-Sonine type containing the Lorenzo-Hartley kernel. A general fractional-order model for the wave equation with the analytical solution is discussed in detail. The general fractional-order formula is accurate and efficient for description of the complex, power-law and memory behaviors for the mining rock.
KEYWORDS
PAPER SUBMITTED: 2018-09-27
PAPER REVISED: 2019-01-20
PAPER ACCEPTED: 2019-01-28
PUBLISHED ONLINE: 2019-06-08
DOI REFERENCE: https://doi.org/10.2298/TSCI180927250C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 3, PAGES [S983 - S987]
REFERENCES
  1. Walsh, J. B., Seismic Wave Attenuation in Rock due to Friction, Journal of Geophysical Research, 71(1966), 10, pp.2591-259
  2. Daniel, I. M., et al., On Wave and Fracture Propagation in rock Media, Experimental Mechanics, 15(1975), 12, pp. 449-457.
  3. Johnson, P. A., et al., Observation and Implications of Nonlinear Elastic Wave Response in Rock, Geophysical Research Letters, 21(1994), 3, pp.165-168
  4. Guyer, R. A., et al., Hysteresis, Discrete Memory, and Nonlinear Wave Propagation in Rock: A New Paradigm, Physical Review Letters, 74(1995), (17), pp.3491
  5. McCall, K. R, Theoretical Study of Nonlinear Elastic Wave Propagation, Journal of Geophysical Research: Solid Earth, 99(1994), B2, pp. 2591-2600.
  6. McCall, K. R., et al., A New Theoretical Paradigm to Describe Hysteresis, Discrete Memory and Nonlinear Elastic Wave Propagation in Rock, Nonlinear Processes in Geophysics, 3(1996), 2, pp.89-101
  7. Yang, X. J., General Fractional Derivatives: Theory, Methods and Applications, New York, CRC Press, 2019
  8. Lorenzo, C. F., et al., The Fractional Trigonometry: with Applications to Fractional Differential Equations and Science, Wiley, New York, 2016

© 2020 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