An Efficient Technique for Solution of Two -Dimensional Fractional Blach-Torrey Equations

Mohammad Alim Rohani, Basher Ahmad Baba Zoi, Asadullah Torabi

Abstract: The main aim of the current paper is to propose an ecient numerical technique for solving two-dimensional space-multi-time fractional BlochTorrey equations. The current research work is a generalization of [6]. The temporal direction is based on the Caputo fractional derivative with multi-order fractional derivative and the spatial directions are based on the RiemannLiouville fractional derivative. Thus, to achieve a numerical technique, the time variable is discretized using a nite difference scheme with convergence order. Also, the space variable is discretized using the nite element method. Furthermore, for the time-discrete and the full-discrete schemes error estimate has been presented to show the unconditional stability and convergence of the developed numerical method. Finally, four test problems have been illustrated to verify the eciency and simplicity of the proposed technique on irregular computational domains.

Keywords: Space fractional equation, Bloch-Torrey equations, Fractional derivative, Convergence analysis, Error estimate, Caputo derivative, Riemann-Liouville fractional