Majid Darehmiraki - DEPARTMENT OF MATHEMATICS, BEHBAHAN KHATAM ALANBIA UNIVERSITY OF TECHNOLOGY, BEHBAHAN, KHOUZESTAN, IRAN
Arezou Rezazadeh - DEPARTMENT OF MATHEMATICS, UNIVERSITY OF QOM, QOM ۳۷۱۶۱۴۶۶۷۱۱, IRAN

In this paper we consider the one-dimensional variable-order time fractional diffusion equation where the order is $ q(x,t)in (0,1) $. One type of Caputo fractional derivative is introduced and to get a numerical technique, the time variable is discretized using a finite difference plan then we use a spectral collocation method to discretize the spatial derivative.‎ ‎In order to show the effectiveness and accuracy of this method‎, ‎some test problems are considered‎, ‎and it is shown that the obtained results are in very good agreement with exact solutions‎.

Partial differential equation, parabolic equation, ‎ variable-order derivative ‎chebyshev spectral collocation method‎