Numerical learning approximation of time-fractional sub diffusion model on a semi-infinite domain

Hajimohammadi, Zeinab; Parand, Kourosh

doi:10.1016/j.chaos.2020.110435

Cited by 8 publications

(1 citation statement)

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“…Hussien ( 2019 ) proposed a collocation method for an approximation of two common delay differential equations of fractional order with generalized LPs basis. Hajimohammadi and Parand ( 2021 ) applied a new learning approximation method of generalized Laguerre least squares support vector regression (GLLSSVR) to obtain the solution of time-fractional sub diffusion model (TFSDM) over a semi-infinite domain. Their new method was a combination of collocation/Galerkin method and a kernel of LSSVR method.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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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.

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Section: Introductionmentioning

confidence: 99%