AUTHOR=Appadu Appanah R. , Kelil Abey S. , Nyingong Ndifon Wikocho 

TITLE=Solving a fractional diffusion PDE using some standard and nonstandard finite difference methods with conformable and Caputo operators

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=10

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1358485

DOI=10.3389/fams.2024.1358485

ISSN=2297-4687

ABSTRACT=<sec><title>Introduction</title><p>Fractional diffusion equations offer an effective means of describing transport phenomena exhibiting abnormal diffusion pat-terns, often eluding traditional diffusion models.</p></sec><sec><title>Methods</title><p>We construct four finite difference methods where fractional derivatives are approximated using either conformable or Caputo operators.</p></sec><sec><title>Results</title><p>Stability of the proposed schemes is analyzed using von Neumann stability analysis, and conditions are established to preserve positivity. Consistency analysis is performed for all methods, and numerical results with fractional parameters (α) set to 0.75, 0.90, 0.95, and 1.0 are presented.</p></sec><sec><title>Discussion</title><p>The rate of convergence in time for the four methods is computed.</p></sec>