On the generalized time fractional reaction–diffusion equation: Lie symmetries, exact solutions and conservation laws
Jicheng Yu, Yuqiang Feng
Abstract
In this paper, Lie symmetry analysis method is applied to the generalized time fractional reaction–diffusion equation. We obtain a conditional symmetric group and some conservation laws of the governing equation. The obtained Lie symmetries are used to reduce the studied fractional partial differential equation to some fractional ordinary differential equations with Riemann–Liouville fractional derivative or Erdélyi-Kober fractional derivative . Furthermore, we obtained asymptotic stable solutions and convergent power series solutions for the reduced equations. The dynamic behavior of these exact solutions is presented graphically.
Topics & Concepts
Fractional calculusMathematicsConservation lawHomogeneous spaceOrdinary differential equationSymmetry (geometry)Partial differential equationMathematical analysisDiffusion equationLie groupDifferential equationMathematical physicsPure mathematicsEconomyEconomicsService (business)GeometryFractional Differential Equations SolutionsNonlinear Waves and SolitonsMathematical and Theoretical Epidemiology and Ecology Models