Burgers' equation

Invariant (physics)

Symmetry (geometry)

Service (business)

Mathematics

Mathematical physics

Lagrangian

Knowledge management

Diffusion equation

Partial differential equation

Fractional calculus

Mathematical analysis

Economy

Economics

Geometry

Computer science

Differential equation

Noether's theorem

Innovation diffusion

Conservation law

Ordinary differential equation

Diffusion process

International Journal of Geometric Methods in Modern Physics

Under study in this paper is a time fractional generalized nonlinear diffusion equation which can be better to express diffusion phenomena than diffusion equation of integer order. Firstly, we apply the symmetry analysis method to find the symmetry of this considered equation. Then some conservation laws can also be constructed through the above obtained symmetry with the help of the Noether’s theorem. Next, we reduce this equation into an ordinary differential equation of fractional order in the symmetry with Erdélyi–Kober fractional differential operator under one-dimensional subalgebras optimal system framework. Finally, some exact solutions contain the invariant solutions have found for this given equation. The results give us a new interpretation of this type diffusion process.

On the generalized time fractional diffusion equation: Symmetry analysis, conservation laws, optimal system and exact solutions