TY  - EJOU
AU  - Veeresha, P. 
AU  - Ilhan, Esin 
AU  - Prakasha, D. G. 
AU  - Baskonus, Haci Mehmet 
AU  - Gao, Wei 

TI  - Regarding on the Fractional Mathematical Model of Tumour Invasion and Metastasis
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2021
VL  - 127
IS  - 3
SN  - 1526-1506

AB  - In this paper, we analyze the behaviour of solution for the system exemplifying model of tumour invasion and
metastasis by the help of <i>q</i>-homotopy analysis transform method (<i>q</i>-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.
KW  - Tumour cell; invasion and metastasis; q-homotopy analysis transform method; Caputo–Fabrizio derivative

DO  - 10.32604/cmes.2021.014988