Author:
Alzahrani Ebraheem O.,Khan Muhammad Altaf
Abstract
<p style='text-indent:20px;'>Prostate cancer worldwide is regarded the second most frequent diagnosed cancer in men with (899,000 new cases) while in common cancer it is the fifth. Regarding the treatment of progressive prostate cancer the most common and effective is the intermittent androgen deprivation therapy. Usually this treatment is effective initially at regressing tumorigenesis, mostly a resistance to treatment can been seen from patients and is known as the castration-resistant prostate cancer (CRPC), so there is no any treatment and becomes fatal. Therefore, we proposed a new mathematical model for the prostate cancer growth with fractional derivative. Initially, we present the model formulation in detail and then apply the fractional operator Atangana-Baleanu to the model. The fractional model will be studied further to analyze and show its existence of solution. Then, we provide a new iterative scheme for the numerical solution of the prostate cancer growth model. The analytical results are validated by considering various values assigned to the fractional order parameter <inline-formula><tex-math id="M1">\begin{document}$ \alpha. $\end{document}</tex-math></inline-formula></p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference25 articles.
1. K. Akakura, N. Bruchovsky, S. L. Goldenberg, P. S. Rennie, A. R. Buckley, L. D. Sullivan.Effects of intermittent androgen suppression on androgen-dependent tumors. Apoptosis and serum prostate-specific antigen, Cancer, 71 (1993), 2782-2790.
2. A. Atangana and D. Baleanu, New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer model, preprint, (2016), arXiv: 1602.03408.
3. A. Atangana and T. Mekkaoui, Capturing complexities with composite operator and differential operators with non-singular kernel, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (2019), 023103, 15 pp.
4. A. Atangana, S. Jain.The role of power decay, exponential decay and Mittag–Leffler functions waiting time distribution: Application of cancer spread, Physica A: Statistical Mechanics and its Applications, 512 (2018), 330-351.
5. R. R. Berges, J. Vukanovic, J. I. Epstein, M. CarMichel, L. Cisek, D. E. Johnson, R. W. Veltri, P. C. Walsh, and J. T. Isaacs.Implication of cell kinetic changes during the progression of human prostatic cancer, Clinical Cancer Research, 1 (1995), 473-480.