Time-space variable-order fractional nonlinear system of thermoelasticity: numerical treatment

Abstract

Abstract This paper focuses on a numerical study of the general time-space variable-order fractional nonlinear problem of thermoelasticity in one dimension using the weighted average nonstandard finite difference (WANSFD). By replacing the second order space derivative with a Riesz fractional variable-order derivative and the time derivative by Caputo fractional variable-order operator in the standard system which arises in thermoelasticity, we obtain this general system. Using a kind of John von Neumann technique, we study the stability of the designed schemes. Also, the truncation error of the introduced schemes is studied. Our numerical treatment is shown graphically. These results expose that WANSFD approach is suitable and effective for solving the proposed system; moreover, it is easy to implement.

Keywords

• Time-space variable-order fractional nonlinear thermoelasticity
• Riesz fractional fractional variable-order derivative
• John von Neumann stability method
• Weighted average nonstandard finite difference methods