| Abstract: |
| The aim of the talk is to present the motivation for considering nonlocal operators in cancer models; address the challenges these operators pose in terms of analysis and numerical simulation; and showcase the observations and results of the numerical experiments.
The tumour microenvironment has a strong influence on tumour cell proliferation and migration. For instant, the cell-cell adhesion induces subdiffusivity; hapotaxis and chemotaxis induces superdiffusivity; and the viscoelasticity of the extracellular matrix substantially affect the spreading, growth, proliferation, migration of the cancer cells.
Fractional operators have undoubtedly exercised their efficiency in modelling complex and intermediate processes like anomalous diffusion (sub and super diffusion) and viscoelasticity. At the same time, the very nature of non-locality of the fractional operators introduces computational complexities and challenges in obtaining existence results. This calls for the analysis of these equations and efficient memory management algorithms.
Fractional operators have shown to outperform the integer order differential equations in capturing effects which are crucial in cancer modelling. Adopting these operators in the modelling could help in better understanding of the development of tumour cells and their dynamics. These in turn will help in devising appropriate treatment methods for cancer patients. |
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