An Efficient Numerical Approach for Fractional Heat Equations with Nonlocal Memory Terms

Sami  Baroudi; Ali  El Mfadel; Abderrazak  Kassidi; M’hamed  Elomari

doi:10.5269/bspm.76574

An Efficient Numerical Approach for Fractional Heat Equations with Nonlocal Memory Terms

Sami Baroudi
Ali El Mfadel Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Morocco.
Abderrazak Kassidi Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Morocco.
M’hamed Elomari Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Morocco.

Resumen

This paper presents a numerical method for solving partial integro-differential equations with weakly singular kernels, using a tempered φ-Caputo fractional derivative of order α ∈ (0, 1). We apply a second-order time discretization and use a tempered fractional integral operator along with piecewise linear interpolation to handle the singularity in the kernel. The stability of the method is analyzed using Von Neumann stability analysis. Finally, numerical examples are provided to demonstrate the effectiveness of the approach.