Optimal Approximation of Fractional Order Brain Tumor Model Using Generalized Laguerre Polynomials

A brain tumor occurs when abnormal cells form within the brain. Glioblastoma (GB) is an aggressive and fast-growing type of brain tumor that invades brain tissue or spinal cord. GB evolves from astrocytic glial cells in the central nervous system. GB can occur at almost any age, but the occurrence increases with advancing age in older adults. Its symptoms may include nausea, vomiting, headaches, or even seizures. GB, formerly known as glioblastoma multiforme, currently has no cure with a high rate of resistance to therapy in clinical treatment. However, treatments can slow tumor progression or alleviate the signs and symptoms. In this paper, a fractional order brain tumor model was considered. The optimal solution of the model was obtained using an optimization method based on operational matrices. The solution to the problem under study was expanded in terms of generalized Laguerre polynomials (GLPs). The study problem was shifted to a system of nonlinear algebraic equations by the use of Lagrange multipliers combined with operational matrices based on GLPs. The analysis of convergence was discussed. In the end, some numerical examples were presented to justify theoretical statements along with the patterns of biological behavior.