6

Mathematical Modeling for Brain Tumors

Including Fractional Operator

Arife Aysun Karaaslan

Üsküdar University, İstanbul, Türkiye

Mathematical modeling is a way of representing real-life problems. Firstly, a

problem is defined and according to the problem, a system can be constructed

using variables. Systems can be solved using different methods. Outcomes give

us a cycle between real life and mathematical life. This cycle is a formulation

and the formulation can be graphs, equations, sometimes inequations etc.

Differential equations may be included in some models while they may not be

in others. They may include statistical terms and regression analysis. But our

models include mathematical structures and ordinary differential equations

or partial differential equations. There are various solution methods but in

this chapter, we will give information about fractional operators. Fractional

operator studies with non-integer order of derivatives and effects of fractional

calculus over brain tumor growth will be examined.

6.1

Introduction

Uncontrolled cell growth and proliferation is referred to as a tumor. Benign

and malignant are the terms used to describe the resulting formation. Be-

nign tumors do not spread to other areas; they are confined to the area in

which they originate. Tumors that are malignant can grow and spread to

other tissues. Malignant growths are referred to as cancer. One or more cell

mutations are the source of cancerous tumors, which typically develop quickly

and uncontrollably. We’ll talk about the unchecked growth and dissemination

of brain tumors. Three stages are present in brain tumors. Gliomas in their

fourth and worst stage are the most deadly tumors. Following a tumor diag-

nosis, treatment is crucial, and “The problem of how gliomas spread” is one of

DOI: 10.1201/9781003461906-6

158