A semi-analytic collocation technique for solving 3D anomalous non-linear thermal conduction problem associated with the Caputo fractional derivative

Abstract

A semi-analytic numerical method is described as an efficient meshless approach for the solution of anomalous non-linear thermal conduction problems in functionally graded materials in which the model results in fractional boundary value problems. The first key feature in this scheme is the derivation and discretization of the fractional derivative at every time step. The second key feature is the trigonometric basis functions (TBFs) as the basis functions were introduced by the need for approximate solutions on boundary conditions with more flexibility in choosing collocation points. Moreover, the approximate solution of the anomalous thermal conduction problems converges to the exact solution as γ is closed to 1 in the full closed time interval for three simulated numerical results.