On analyzing two dimensional fractional order brain tumor model based on orthonormal Bernoulli polynomials and Newton's method

Authors

DOI:

https://doi.org/10.11121/ijocta.1409

Keywords:

Brain tumor, Operational matrix, Orthonormal Bernoulli polynomials, Fractional Caputo derivative

Abstract

Recently, modeling problems in various field of sciences and engineering with the help of fractional calculus has been welcomed by researchers. One of these interesting models is a brain tumor model. In this framework, a two dimensional expansion of the diffusion equation and glioma growth is considered. The analytical solution of this model is not an easy task, so in this study, a numerical approach based on the operational matrix of conventional orthonormal Bernoulli polynomials (OBPs) has been used to estimate the solution of this model. As an important advantage of the proposed method is to obtain the fractional derivative in matrix form, which makes calculations easier. Also, by using this technique, the problem under the study is converted into a system of nonlinear algebraic equations. This system is solved via Newton's method and the error analysis is presented. At the end to show the accuracy of the work, we have examined two examples and compared the numerical results with other works.

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Author Biographies

Iman Masti, Faculty of Mathematics and Statistics, Malayer University, Malayer Iran

Iman Masti is a Ph.D. student at Department of Mathematical Sciences, Malayer University. His research interests include: bio-mathematics, fractional differential equations and approximation methods.

Khosro Sayevand, Faculty of Mathematics and Statistics, Malayer University, Malayer Iran

Khosro Sayevand is a full professor in applied mathematics at the Department of Mathematical Sciences, Malayer University. His research interests include: fractional calculus, modelling, perturbation theory and linear programming.

Hossein Jafari, Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa

Hossein Jafari is a full professor in applied mathematics. His research interests include: bio-mathematics, fractional differential equations, Lie Symmetry and approximation methods.

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Published

2023-11-08
CITATION
DOI: 10.11121/ijocta.1409
Published: 2023-11-08

How to Cite

Masti, I., Khosro Sayevand, & Jafari, H. (2023). On analyzing two dimensional fractional order brain tumor model based on orthonormal Bernoulli polynomials and Newton’s method. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 14(1), 12–19. https://doi.org/10.11121/ijocta.1409

Issue

Vol. 14 No. 1 (2024): IJOCTA

Section

Research Articles

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Copyright (c) 2023 Iman Masti, Khosro Sayevand, Hossein Jafari

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