University of Guilan Journal of Mathematical Modeling 2345-394X 10 3 2022 09 01 Numerical solution of space-time variable fractional order advection-dispersion equation using radial basis functions 549 562 5561 10.22124/jmm.2022.21325.1868 EN Abolfazl Soltanpour Moghadam Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran Maryam Arabameri Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran Mahdiar Barfeie Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, Iran Journal Article 2021 12 18 This paper aims to advance the radial basis function method for solving space-time variable-order fractional partial differential equations. The fractional derivatives for time and space are considered in the Coimbra and the Riemann-Liouville sense, respectively. First, the time-variable fractional derivative is discretized through a finite difference approach. Then, the space-variable fractional derivative is approximated by radial basis functions. Also, we advance the Rippa algorithm to obtain a good value for the shape parameter of the radial basis functions. Results obtained from numerical experiments have been compared to the analytical solutions, which indicate high accuracy and efficiency for the proposed scheme. Advection-dispersion equation radial basis functions Coimbra fractional derivative Riemann-Liouville fractional derivative https://jmm.guilan.ac.ir/article_5561_3886565e31d080929ac977588158e79c.pdf