THERMAL SCIENCE

International Scientific Journal

Feng GaoORCID

AN ANALYTICAL SOLUTION FOR SOLVING A NEW WAVE EQUATION WITHIN LORENZO-HARTLEY KERNEL

ABSTRACT
In this article we investigate the general fractional-order derivatives of the Riemann-Liouville type via Lorenzo-Hartley kernel, general fractional-order integrals and the new general fractional-order wave equation defined on the definite domain with the analytical solution.
KEYWORDS
general fractional-order derivative, general fractional-order integral, general fractional-order wave equation, analytical solution
PAPER SUBMITTED: 2018-10-11
PAPER REVISED: 2019-01-11
PAPER ACCEPTED: 2019-01-28
PUBLISHED ONLINE: 2019-06-08
DOI REFERENCE: https://doi.org/10.2298/TSCI181011258G
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE No. 6, PAGES [3739 - 3744]
REFERENCES
[1] Yang, X. J., General Fractional Derivatives: Theory, Methods and Applications, New York, CRC Press, 2019
[2] Caputo, M., et al., A New Definition of Fractional Derivative without Singular Kernel, Progress in Fractional Differentiation and Applications, 1 (2015), 2, pp.73-85
[3] Mittag-Leffler, G., Sur la Représentation Analytique d'une Branche Uniforme d'une Fonction Monogène: Cinquième Note, Acta mathematica, 29(1905), 1, 101-181
[4] Rabotnov, Y., Equilibrium of an Elastic Medium with After-Effect, Fractional Calculus and Applied Analysis, 17(2014), 3, pp.684-696, 10.2478/s13540-014-0193-1
[5] Miller, K. S., et al., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993
[6] Yang, X. J., et al., Fundamental Solutions of Anomalous Diffusion Equations with the Decay Exponential Kernel, Mathematical Methods in the Applied Sciences, 2019, April, 10.1002/mma.5634
[7] Yang, X. J., et al., Fundamental Solutions of the General Fractional-Order Diffusion Equations, Mathematical Methods in the Applied Sciences, 41(2018), 18, pp.9312-9320, 10.1002/mma.5341
[8] Lorenzo, C. F., et al., Generalized Functions for the Fractional Calculus, Critical Reviews in Biomedical Engineering, 36(2008), 1, pp.39-55, 10.1615/critrevbiomedeng.v36.i1.40
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An analytical solution for solving a new wave equation within Lorenzo-Hartley kernel

© 2026 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