Mathematical Modeling for Brain Tumors Including Fractional Operator 159

the main issues that arises. This means that the tumor is not the only thing

being imaged. It is the spread of the cell, which may not be observed by imag-

ing techniques. As a result, researchers concentrated on understanding how

gliomas grow. Growth of tumor models, a developing study in glioma research,

became a field. Researchers study mathematical models to better understand

the glioma growth process. Mathematical models are utilized to comprehend

complex structures while studying processes and diseases. Theoretical models

mainly focus on the total amount of cells in a tumor and assume exponential

growth, Gompertzian, or logistic.

6.2

Obtaining the Models

A mathematical model is a language for describing a system. This description

may be made, among other things, by mathematical formalism and abstrac-

tion, which may allow for extrapolation beyond situations that were initially

examined, quantitative predictions, and/or inference of mechanisms [1]. Three

basic steps make up the procedure of mathematical modeling: first, a prob-

lem set from the actual world is formulated as a mathematical issue; this,

along with any presumptions made, is the mathematical model. After the

mathematical difficulty is resolved and the answer is eventually applied to

the original situation, the outcomes that the model assessed may be deci-

phered and applied to assist in resolving the original issue [2]. The behavior

of developing gliomas under scientific investigation can possibly be described

mathematically in the case of gliomas. Murray’s diffusion model is the first

glioma development model [3–5].

6.3

Some Solution Methods for Mathematical Models

There are different solution methods for solving mathematical models. All have

some advantages and disadvantages compared to each other. In this section,

we give some information about basic solution methods; finite element, finite

difference, and finite volume.

6.3.1

Finite Element Method

A numerical analytical method for approximating solutions to a wide range

of engineering issues is the finite element method (FEM) [6]. The governing

equations of a problem can be approximated piecewise using a finite element