Mathematical Modeling of Cancer Tumor Dynamics with Multiple Fuzzification Approaches in Fractional Environment
摘要
Cancer progression arises from the accumulation of genetic mutations in cell proliferation control genes. To efficiently treat these defected cells and restrict their proliferation, numerous cancer tumor patterns have been extensively studied in the literature, but mainly considering crisp scenario (without uncertainties). The current study aims to model and explore fuzzy-fractional cancer tumor dynamics with three different cell killing rates derived from practical situations. Furthermore, various fuzzification strategies namely Gaussian, Trapezoidal, and Triangular fuzzy numbers are utilized to introduce uncertainties in phenomena. Current modeling of cancer tumor results in comprehensive investigation that not only encompasses the imprecision involved in real-time data but also deals with non-integer order and non-traditional derivatives. An innovative algorithm is also introduced by combining diverse homotopies with the perturbation technique and Aboodh transform to create a hybrid mechanism for recovering solutions of such complex model. The effectiveness of proposed methodology is evaluated through detailed numerical experiments. In the subsequent stage, the convergence and validity are assessed by residual errors, graphical illustrations, and contours throughout the fractional domain. This approach allows effective representation of tumor heterogeneity and enables better understanding, prediction, and optimization of treatment strategies. The study reveals that in case of time-dependent killing rate, tumor cell decreases quadratically with time. It is also noted that when killing rate is inversely proportional to the position, rapid elimination of cells near the tumor center is seen. Moreover, quadratic relationship between cell concentration and killing rate leading to a self-limiting effect. The convergence of solution profiles at \( \alpha =1 \) indicated a transition to crisp form when the membership function reaches its maximum value. The end results endorse that fuzzification of models provides a more comprehensive and flexible environment for analyzing complex dynamics of different systems generated in science and engineering.