Abstract
In this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.
Highlights
Mathematical models for tumour growth have been extensively studied in the literature, and the main purpose of these studies is to understand the mechanism of the disease and to predict its future behavior
We derive the approximate solution of the system given by Equation (36) using the Sumudu transform operator given by Equation (9)
The solution of the alternative models were obtained using an iterative scheme—for the Caputo-Fabrizio-Caputo fractional order derivative based in the Laplace transform and for the Atangana-Baleanu-Caputo fractional order derivative based in the Sumudu transform
Summary
Mathematical models for tumour growth have been extensively studied in the literature, and the main purpose of these studies is to understand the mechanism of the disease and to predict its future behavior These models are governed by ordinary differential equations; the local differentiation has failed to portray real world problems due to the lack of non-locality effect into mathematical formulation; to solve them, mathematicians introduced the concept of differentiation with non-local operators. In these models, the fractional order equations are related to systems with memory that exists in the biological systems. The fractional order equations are related to systems with memory that exists in the biological systems Another important area of application of the FC is the chaos theory. The third equation illustrates the stimulation of the immune system by the tumour cells with tumour specific antigens [46]
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