Mathematical modelling of growth of tumour cells with chemotherapeutic cells by using Yang–Abdel–Cattani fractional derivative operator

Abstract

Cancer is a fatal disease for a very long time. It has its own history. Now it has become one of the major reasons for death due to its various types. Researchers, scientists and doctors are trying to find out the success and minimize the death rate in this field. The fact is, cancer treatment is only effective when it has been diagnosed at a very early stage. Therefore, cancer is a kind of provocative topic for analysis. In this paper, we have shown the growth of cancer cells, normal cells along with chemotherapeutic cells. We have shown that the effect of chemotherapeutic drugs is highest at the centre of tumour affected area. We have used the Yang–Abdel–Cattani fractional operator with Laplace transform for all numeric calculations. Apart from numerical calculations, we have also shown the graphical representation of cell growth.

Keywords

• Cancer
• chemotherapy
• mathematical model
• Laplace transform
• existence and uniqueness
• Primary 92B05