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A study on brain tumor dynamics in two-dimensional irregular domain with variable-order time-fractional derivative
Harshad Sakariya1, Ravi Shankar Prasad1, Sushil Kumar1
1Department of Mathematics, S. V. National Institute of Technology, Surat 395007, Gujarat, India.
Computer Methods and Programs in Biomedicine
|March 16, 2025
Summary
This study introduces a novel brain tumor growth model using variable-order time-fractional derivatives. Findings reveal how fractional orders and mutation rates impact tumor dynamics, offering new insights for treatment.
Area of Science:
- Computational Biology
- Mathematical Oncology
- Biophysics
Background:
- Brain tumor growth modeling is complex.
- Accurate models are crucial for understanding tumor dynamics and developing treatments.
Purpose of the Study:
- Develop and analyze a brain tumor growth model with variable-order time-fractional derivatives.
- Investigate the influence of fractional orders, mutation rates, and growth parameters on tumor dynamics.
Main Methods:
- Employed finite difference and Gaussian radial basis functions (Kansa's method).
- Performed Ulam-Hyers stability analysis and convergence analysis.
- Validated the computational approach through code verification.
Main Results:
- Numerical simulations revealed novel tumor cell dynamics influenced by fractional effects.
- Variable-order time-fractional derivatives impact tumor cell population growth.
- Mutation and growth parameters significantly affect tumor behavior.
Conclusions:
- Variable-order time-fractional derivatives introduce memory effects in brain tumor models.
- Fractional-order parameters are vital for accurate tumor growth modeling.
- Findings may aid in predicting tumor progression and guiding targeted therapies.
Keywords:
Brain tumor modelCaputo fractional derivativeFinite difference methodRadial basis functionsVariable order time fractional derivativeMore Related Videos
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