Boundary Value Problem of Space-Time Fractional Advection Diffusion Equation

Elsayed I. Mahmoud () and Temirkhan S. Aleroev
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Elsayed I. Mahmoud: Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
Temirkhan S. Aleroev: Department of Applied Mathematics, Moscow State University of Civil Engineering, Yaroslavskoe Shosse, 26, Moscow 129337, Russia

Mathematics, 2022, vol. 10, issue 17, 1-12

Abstract: In this article, the analytical and numerical solution of a one-dimensional space-time fractional advection diffusion equation is presented. The separation of variables method is used to carry out the analytical solution, the basis of the system eigenfunction and their corresponding eigenvalue for basic equation is determined, and the numerical solution is based on constructing the Crank-Nicolson finite difference scheme of the equivalent partial integro-differential equations. The convergence and unconditional stability of the solution are investigated. Finally, the numerical and analytical experiments are given to verify the theoretical analysis.

Keywords: space-time fractional advection diffusion equation; Riemann–Liouville fractional derivative; Caputo fractional derivative; Crank–Nicolson finite difference scheme; stability; convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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