Similarity solutions and the computation formulas of a nonlinear fractional-order generalized heat equation

Abstract

A generalized nonlinear heat equation with the fractional derivative is proposed, whose similarity solutions are derived from a type of special scalar transformation with two parameters. With the help of separated variable method, two special series solutions of the standard heat equation are obtained. Finally, through computation of the left Riemann–Liouville fractional derivative, we obtain two approximated computation formulas of the factional-order ordinary differential equation which could be used to calculate the numerical solutions of the generalized nonlinear heat conduction equation.