On the Dynamics, Invariance Analysis, Exact Reductions, Series Solutions and Conservation Laws for the Time-Fractional Spherically Symmetric Brain Tumor Model

The Lie symmetry analysis for the time-fractional spherically symmetric brain tumor equation in spherical coordinates, assuming the killing rates are functions of tumor-cells is studied. The classification with regard to the net killing rate is obtained. The underlying equation is transformed into a fractional ordinary differential equation using the Erde´ lyi-Kober fractional differential operator. The explicit series solutions are obtained with its convergence analysis. The graphs of the solutions are given from which we may extract the behaviour of the solutions. Finally, we construct the conservation laws for the time-fractional brain tumor equation.