A hybrid computational framework for fractional cancer diffusion models in uncertain settings

Area of Science:

• Mathematical Oncology
• Computational Biology
• Applied Mathematics

Background:

• Fractional calculus models are vital for cancer dynamics, but incorporating fuzzy logic remains an innovation gap.
• Existing crisp models lack the ability to represent uncertainty inherent in biological systems like cancer growth.

Purpose of the Study:

• To develop and solve a novel fuzzy-fractional diffusion cancer model using a hybrid He-Laplace algorithm.
• To analyze cancer diffusion dynamics under uncertainty using triangular fuzzy numbers.
• To explore the impact of time-dependent and space-dependent killing rates on tumor progression.

Main Methods:

• A hybrid algorithm combining homotopy, perturbation techniques, and Laplace transforms was developed.
• The Liouville-Caputo fractional derivative was employed within a fuzzy environment.
• Numerical solutions were obtained for both lower and upper bounds of fuzzy numbers, with residual errors calculated for validation.

Main Results:

• The fuzzy-fractional model successfully captured cancer diffusion dynamics and tumor heterogeneity.
• Numerical simulations provided insights into the effects of different fractional orders and killing rate scenarios.
• 2D/3D visualizations and contour diagrams confirmed the method's accuracy and applicability in a fuzzy context.

Conclusions:

• The developed fuzzy-fractional diffusion model offers a powerful tool for analyzing complex cancer tumor dynamics.
• This approach enhances the understanding, prediction, and optimization of cancer therapies by incorporating uncertainty.
• The method demonstrates significant potential for application in various scientific and biological modeling challenges.