THERMAL SCIENCE
International Scientific Journal
APPROXIMATE ANALYTIC SOLUTION FOR MULTI-DIMENSIONAL FRACTIONAL WAVE-LIKE EQUATION
ABSTRACT
The fractional power series method is used to solve 2- and 3-D fractional wave-like models with variable coefficients. The fractional derivatives are described in the Caputo sense. Two examples are considered to show the effectiveness and convenience of the method.
KEYWORDS
PAPER SUBMITTED: 2019-04-04
PAPER REVISED: 2019-10-20
PAPER ACCEPTED: 2019-10-20
PUBLISHED ONLINE: 2020-06-21
THERMAL SCIENCE YEAR
2020, VOLUME
24, ISSUE
Issue 4, PAGES [2645 - 2652]
- Caputo, M., Linear Models of Dissipation Whose Q is almost Frequency Independent Part II, Geophysical Journal International, 13 (1967), 5, pp. 529-539
- Li, C., et al., On Riemann-Liouville and Caputo Derivatives, Discrete Dynamics in Nature and Society, 2011 (2011), 1, pp. 309-323
- Yang, X. J., et al., Local Fractional Integral Transforms and their Applications, Academic Press, New York, USA, 2015
- Yan, J. P., Li, C.P., On Chaos Synchronization of Fractional Differential Equations, Chaos, Solitons Fractals, 32 (2007), 2, pp. 725-735
- Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006
- Jumarie, G., Table of Some Basic Fractional Calculus Formulae Derived from a Modified Riemann-Liouville Derivative for Non-Differentiable Functions, Applied Mathematics Letters, 22 (2009), 3, pp. 378-385
- Molliq, Y. R., et al., Variational Iteration Method for Fractional Heat- and Wave-Like Equations, Nonlinear Analysis: Real World Applications, 10 (2009), 3, pp. 1854-1869
- Momani, S., Analytical Approximate Solution for Fractional Heat-Like and Wave-Like Equations with Variable Coefficients Using the Decomposition Method, Applied Mathematics and Computation, 165 (2005), 2, pp. 459-472
- Al-Hayani,W., Daftardar-Jafari Method for Fractional Heat-Like and Wave-Like Equations with Variable Coefficients, Applied Mathematics, 8 (2017), 2, pp. 215-228
- Andrezei, H., Multi-Dimensional Solutions of Space-Time-Fractional Diffusion Equations, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 458 (2002), 2018, pp. 429-450
- El-Ajou, A., et al., New Results on Fractional Power Series: Theories and Applications, Entropy, 15 (2013), 12, pp. 5305-5323
- Shou, D. H., He, J. H., Beyond Adomian Methods: The Variational Iteration Method for Solving Heat-Like and Wave-Like Equations with Variable Coefficients, Physics Letters A, 73 (2007), 1, pp. 1-5
- Adomian, G., A Review of the Decomposition Method in Applied Mathematics, Journal of mathematical analysis and applications, 135 (1988), 2, pp. 501-544
- Podlubny, I., Fractional Differential Equations, Academic Press New York, NY, USA, 1999
- He, J. H., Ji, F. Y., Taylor Series Solution for Lane-Emden Equation, Journal of Mathematical Chemistry, 57 (2019), 8, pp. 1932-1934
- He, J. H., The Simplest Approach to Nonlinear Oscillators, Results in Physics, 15 (2019), 102546
- Yang, A. M., et al., Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets, Abstract and Applied Analysis, 2013 (2013), ID 351057
- Li, Z. B., Zhu, W. H., Fractional Series Expansion Method for Fractional Differential Equations, International Journal of Numerical Methods for Heat & Fluid Flow, 25 (2015), 7, pp. 1525-1530
- He, J. H., et al., A New Fractional Derivative and Its Application to Explanation of Polar Bear Hairs, Journal of King Saud Universe Science, 28 (2016), 2, pp. 190-192
- He, J. H., Li, Z. B., A Fractional Model for Dye Removal, Journal of King Saud Universe Science, 28 (2016), 1, pp. 14-16
- Liu, H. Y., et al., Fractional Calculus for Nanoscale Flow and Heat Transfer, International Journal of Numerical Methods for Heat & Fluid Flow, 24 (2014), 6, pp. 1227-1250
- Liu, H. Y., et al., A Fractional Nonlinear System for Release Oscillation of Silver Ions from Hollow Fibers, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 1, pp. 88-92
- Ren, Z. F., et al., He's Multiple Scales Method for Nonlinear Vibrations, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1708-1712
- Yang, J. J., Wang, S. Q., An Improved Homotopy Perturbation Method for Solving Local Fractional Non-linear Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 918-927
- He, J. H., Ji, F. Y. Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
- He, J. H., A Simple Approach to One-Dimensional Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), 113565
- Wang, Y., et al., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, 1950047
- Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, ID 1950134
- Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), 6, ID 1850086
- Wang, Y., Deng, Q., Fractal Derivative Model For Tsunami Travelling, Fractals, 27 (2019), 1, 1950017
- Sun, J. S., Analytical Approximate Solutions Of (N+1)-Dimensional Fractal Harry Dym Equations, Fractals, 26 (2018), 6, ID 1850094
- Sun, J. S., Approximate Analytic Solutions of Multi-Dimensional Fractional Heat-Like Models with Variable Coefficients, Thermal Science, 23 (2019), 6B, pp. 3725-3729