On integrability of the time fractional nonlinear heat conduction equation

Abstract

Under investigation in this letter is a time fractional nonlinear heat conduction equation which usually appears in mathematics physics, integrable system, fluid mechanics and nonlinear areas, by means of applying the fractional symmetry group method with the sense of Riemann-Liouville (R-L)fractional derivative. First of all, we use the fractional symmetry group method to obtain symmetries of the time fractional nonlinear heat conduction equation. Second, according to the above find symmetries, this equation can be reduced to a fractional ordinary differential equation. Moreover, invariant solutions of the time fractional nonlinear heat conduction equation are yielded. Finally, with the aid of the Ibragimov theorem, the conservation laws are also find to the time fractional nonlinear heat conduction equation. These new results are an effective complement to existing knowledge.