DOI: 10.12732/ijam.v38i2.7
STUDY THE STABILITY OF THE
FOURIER TRANSFORM OF THE
VARIABLE-ORDER TIME FRACTIONAL
SEMI-LINEAR DIFFUSION EQUATION
Mohamed El-hadi Smakdji 1,§, Ammar Derbazi 2,
Mohamed Dalah 3, Abdelwahab Zarour 4
1,3,4 Department of Mathematics
Faculty of Exact Sciences
University Constantine 1: Fr`eres Mentouri
ALGERIA
2 University Bordi-Bou Arriridj
Department of Mathematics
34030, ALGERIA
Abstract. In this research, we present a finite difference scheme (FDS) aimed at exploring the linear time and space fractional advection equation. To approximate the fractional derivatives, we utilize the fractional Taylor series for u (x, t) at t_j and x_i. Our primary focus lies in constructing a numerical scheme (NS) for the mathematical model. Following this, we delve into an examination of the stability and convergence of our NS. Ultimately, we conduct numerical simulations of the fractional advection equation using the FDM across different fractional parameter values. The outcomes of these simulations demonstrate satisfactory convergence, thereby confirming the efficacy of the proposed algorithm.
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DOI: 10.12732/ijam.v38i2.7
Source: International Journal of
Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 2
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