Malaysian Journal of Mathematical Sciences, September 2025, Vol. 19, No. 3
On the Dynamics, Invariance Analysis, Exact Reductions, Series Solutions and Conservation Laws for the Time-Fractional Spherically Symmetric Brain Tumor Model
Zinat, N., Kara, A. H., and Zaman, F. D.
Corresponding Email: Abdul.Kara@wits.ac.za
Received date: 19 November 2024
Accepted date: 24 April 2025
Abstract:
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 Erd$\acute{e}$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.
Keywords: brain tumor model; invariance analysis; conservation laws
