Document Type : Research Paper


1 Department of Management, International Institute of Business Studies, Airport Campus Bangalore.

2 Deparment of Mathematics & Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science & Technology, Chennai, India.

3 Department of Mathematics, Maharishi Markandeshwar University, Mullana, Ambala, Haryana, India.

4 Department of Mathematics, Baba Ghulam Shah Badshah University, Rajouri Jammu, India.

5 Poornima College of Engineering, Jaipur-3020222, India.

6 Department of Mathematics, Anand International College of Engineering, Jaipur, 303012, Rajasthan, India.


In this present study, the tumor growth model using the Gompertz equation with the Allee effect is developed under a fuzzy environment using the Generalized Hukuhara Derivative  (GHD) approach. To capture the tumor growth patterns with the Allee threshold, the parameters present in the model vary from time to time, and in real life, it is very difficult to estimate the exact cell count. In this vague situation, the initial condition, coefficient, and both together are taken as the fuzzy number. In this paper, the  GHD  approach is used to solve the fuzzy tumor growth model in which four different cases are considered with respect to (i)-gH differentiability and (ii)-gH differentiability concept. The main objective of this study is to present a significant reduction in uncertainty while modeling the tumor growth in a fuzzy environment with the Allee effect. Finally, the proposed model and technique are illustrated by numerical simulation and analysis of tumor growth is conducted.


Main Subjects

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