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# Regarding on the Fractional Mathematical Model of Tumour Invasion and Metastasis

P. Veeresha1, Esin Ilhan2, D. G. Prakasha3, Haci Mehmet Baskonus4, Wei Gao5,*
1 Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India
2 Faculty of Engineering and Architecture, Kirsehir Ahi Evran University, Kirsehir, 40500, Turkey
3 Department of Mathematics, Faculty of Science, Davangere University, Shivagangothri, Davangere, 577007, India
4 Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa, 63050, Turkey
5 School of Information Science and Technology, Yunnan Normal University, Yunnan, 650500, China
* Corresponding Author: Wei Gao. Email:
(This article belongs to this Special Issue: Mathematical Aspects of Computational Biology and Bioinformatics)

Computer Modeling in Engineering & Sciences 2021, 127(3), 1013-1036. https://doi.org/10.32604/cmes.2021.014988

Received 14 November 2020; Accepted 09 February 2021; Issue published 24 May 2021

### Abstract

In this paper, we analyze the behaviour of solution for the system exemplifying model of tumour invasion and metastasis by the help of q-homotopy analysis transform method (q-HATM) with the fractional operator. The analyzed model consists of a system of three nonlinear differential equations elucidating the activation and the migratory response of the degradation of the matrix, tumour cells and production of degradative enzymes by the tumour cells. The considered method is graceful amalgamations of q-homotopy analysis technique with Laplace transform (LT), and Caputo–Fabrizio (CF) fractional operator is hired in the present study. By using the fixed point theory, existence and uniqueness are demonstrated. To validate and present the effectiveness of the considered algorithm, we analyzed the considered system in terms of fractional order with time and space. The error analysis of the considered scheme is illustrated. The variations with small change time with respect to achieved results are effectively captured in plots. The obtained results confirm that the considered method is very efficient and highly methodical to analyze the behaviors of the system of fractional order differential equations.

### Keywords

Tumour cell; invasion and metastasis; q-homotopy analysis transform method; Caputo–Fabrizio derivative

Veeresha, P., Ilhan, E., Prakasha, D. G., Baskonus, H. M., Gao, W. (2021). Regarding on the Fractional Mathematical Model of Tumour Invasion and Metastasis. CMES-Computer Modeling in Engineering & Sciences, 127(3), 1013–1036.

### Citations

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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