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Article

Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method

by
Imtiaz Ahmad
1,
Hijaz Ahmad
2,
Phatiphat Thounthong
3,
Yu-Ming Chu
4,5,* and
Clemente Cesarano
6
1
Department of Mathematics, University of Swabi, Swabi 23430, Pakistan
2
Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
3
Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, Bangkok 10800, Thailand
4
Department of Mathematics, Huzhou University, Huzhou 313000, China
5
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changasha, University of Science & Technology, Changsha 410114, China
6
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(7), 1195; https://doi.org/10.3390/sym12071195
Submission received: 22 June 2020 / Revised: 13 July 2020 / Accepted: 17 July 2020 / Published: 19 July 2020
(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Applications)
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Abstract

Fractional differential equations depict nature sufficiently in light of the symmetry properties which describe biological and physical processes. This article is concerned with the numerical treatment of three-term time fractional-order multi-dimensional diffusion equations by using an efficient local meshless method. The space derivative of the models is discretized by the proposed meshless procedure based on the multiquadric radial basis function though the time-fractional part is discretized by Liouville–Caputo fractional derivative. The numerical results are obtained for one-, two- and three-dimensional cases on rectangular and non-rectangular computational domains which verify the validity, efficiency and accuracy of the method.
Keywords: three-term time-fractional diffusion equation; Liouville–Caputo derivative; meshless method; radial basis function three-term time-fractional diffusion equation; Liouville–Caputo derivative; meshless method; radial basis function

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MDPI and ACS Style

Ahmad, I.; Ahmad, H.; Thounthong, P.; Chu, Y.-M.; Cesarano, C. Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method. Symmetry 2020, 12, 1195. https://doi.org/10.3390/sym12071195

AMA Style

Ahmad I, Ahmad H, Thounthong P, Chu Y-M, Cesarano C. Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method. Symmetry. 2020; 12(7):1195. https://doi.org/10.3390/sym12071195

Chicago/Turabian Style

Ahmad, Imtiaz, Hijaz Ahmad, Phatiphat Thounthong, Yu-Ming Chu, and Clemente Cesarano. 2020. "Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method" Symmetry 12, no. 7: 1195. https://doi.org/10.3390/sym12071195

APA Style

Ahmad, I., Ahmad, H., Thounthong, P., Chu, Y.-M., & Cesarano, C. (2020). Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method. Symmetry, 12(7), 1195. https://doi.org/10.3390/sym12071195

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