THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Sheng Zhang

,

Ran Zhu

,

Luyao Zhang

EXACT SOLUTIONS OF TIME FRACTIONAL HEAT-LIKE AND WAVE-LIKE EQUATIONS WITH VARIABLE COEFFICIENTS

ABSTRACT
In this paper, a variable-coefficient time fractional heat-like and wave-like equation with initial and boundary conditions is solved by the use of variable separation method and the properties of Mittag-Leffler function. As a result, exact solutions are obtained, from which some known special solutions are recovered. It is shown that the variable separation method can also be used to solve some others time fractional heat-like and wave-like equation in science and engineering.
KEYWORDS
heat-like and wave-like equation, variable separation method, exact solution, Mittag-Leffler function
PAPER SUBMITTED: 2015-11-12
PAPER REVISED: 2016-02-01
PAPER ACCEPTED: 2016-02-18
PUBLISHED ONLINE: 2016-09-24
DOI REFERENCE: https://doi.org/10.2298/TSCI16S3689Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S689 - S693]
REFERENCES
  1. Shawagfeh, N. T., Analytical Approximate Solutions for Non-Linear Fractional Differential Equations, Applied Mathematics and Computation, 131 (2002), 2, pp. 517-529
  2. Das, S., Kumar, R., Fractional Diffusion Equations in the Presence of Reaction Terms, Journal of Computational Complexity and Applications, 1 (2015), 1, pp. 15-21
  3. Wu, G. C., Baleanu D., Discrete Fractional Logistic Map and Its Chaos, Non-Linear Dynamics, 75 (2014), 1, pp. 283-287
  4. Wu, G. C., et al., Lattice Fractional Diffusion Equation in Terms of a Riesz-Caputa Difference, Physica A, 438 (2015), 1, pp. 283-287
  5. Khan, H., et al., Existence and Uniqueness Results for Coupled System of Fractional q-Difference Equations with Boundary Conditions, Journal of Computational Complexity and Applications, 1 (2015), 2, pp. 79-88
  6. Yang, X. J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science, 17 (2013), 2, pp. 625-628
  7. Yang, X. J., et al., Fractal Boundary Value Problems for Integral and Differential with Local Fractional Operators, Thermal Science, 19, (2015), 3, pp. 959-966
  8. Cui, L. X., et al., New Exact Solutions of Fractional Hirota-Satsuma Coupled Korteweg-de Vries Equations, Thermal Science, 19 (2015), 4, pp. 1173-1176
  9. Zhang, S., et al., Variable Separation Method for Non-Linear Time Fractional Biological Population Model, International Journal of Numerical Methods for Heat & Fluid Flow, 25 (2015), 7, pp. 1531-1541
  10. Liu, Y., et al., Multi-Soliton Solutions of the Forced Variable-Coefficient Extended Korteweg-de Vries Equation Arisen in Fluid Dynamics of Internal Solitary Waves, Non-Linear Dynamics, 66 (2011), 4, pp. 575-587
  11. Secer, A., Approximate Analytic Solution of Fractional Heat-Like and Wave-Like Equations with Variable Coefficients Using the Differential Transform Method, Advances in Difference Equations, 2012, (2012), 1, ID 198
  12. Momani, S., Approximate Analytic 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
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Exact solutions of time fractional heat-like and wave-like equations with variable coefficients

© 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