Symmetry properties, exact solution and conservation laws of time-fractional Zeldovich-Frank-Kamenetskii equation

The article focuses on investigating Lie symmetry analysis of the time-fractional Zeldovich-Frank-Kamenetskii equation with Riemann-Liouville derivative. The fractional reaction-diffusion equation describes how planar laminar premixed flames spread in combustion theory. The use of the Lie method is also illustrated to obtain Lie symmetry generators, symmetry reduction solutions, invariant properties, and conservation laws. Furthermore, we convert the time-fractional Zeldovich-Frank-Kamenetskii equation to a nonlinear fractional ordinary differential equation (ODE) with Erd\'{e}lyi-Kober derivative using its Lie point symmetries. This decreased fractional ODE is investigated by explicit power series. In addition, some figures for the obtained explicit solution are presented.

کلیدواژه ها:

fractional differential equation ، Zeldovich-Frank-Kamenetskii equation ، Lie symmetry ، Explicit solutions ، Ibragimov method ، Conservation laws