Quantum mechanics

Theoretical physics

Spacetime

Mathematical physics

Biology

Power series

Differential equation

Applied mathematics

Classical mechanics

Noether's theorem

Paleontology

Physics

Nonlinear system

Mathematics

Political science

Homogeneous space

Conservation law

Mathematical analysis

Geometry

Series (stratigraphy)

Ordinary differential equation

Symmetry (geometry)

Fractional calculus

Physica A Statistical Mechanics and its Applications

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space–time fractional nonlinear evolution equations with Riemann–Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi–Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Lie symmetry analysis, explicit solutions and conservation laws for the space–time fractional nonlinear evolution equations