Application of Symmetry Analysis and Conservation Laws to Fractional-Order Nonlinear Conduction-Diffusion Model

This study is aimed to perform Lie symmetry analysis of the nonlinear fractional-order conduction-diffusion Buckmaster model (BM), which involves the Riemann-Liouville (R-L) derivative of fractional-order ‘β’. We are going through symmetry reduction to convert the fractional partial differential equation into a fractional ordinary differential equation. The fractional derivatives of the converted differential equations are evaluated with the help of Erdelyi-Kober (E-K) fractional operators. The power series solution and its convergence are analyzed with Implicit theorem. Conservation laws of the physical model are obtained for consistency of system by Noether’s theorem.