An Overview of Mathematical Modelling in Cancer Research: Fractional Calculus as Modelling Tool

Lourenço Côrte Vieira, Rafael S. Costa, Duarte Valério

Research output: Contribution to journalReview articlepeer-review

3 Citations (Scopus)
54 Downloads (Pure)


Cancer is a complex disease, responsible for a significant portion of global deaths. The increasing prioritisation of know-why over know-how approaches in biological research has favoured the rising use of both white- and black-box mathematical techniques for cancer modelling, seeking to better grasp the multi-scale mechanistic workings of its complex phenomena (such as tumour-immune interactions, drug resistance, tumour growth and diffusion, etc.). In light of this wide-ranging use of mathematics in cancer modelling, the unique memory and non-local properties of Fractional Calculus (FC) have been sought after in the last decade to replace ordinary differentiation in the hypothesising of FC’s superior modelling of complex oncological phenomena, which has been shown to possess an accumulated knowledge of its past states. As such, this review aims to present a thorough and structured survey about the main guiding trends and modelling categories in cancer research, emphasising in the field of oncology FC’s increasing employment in mathematical modelling as a whole. The most pivotal research questions, challenges and future perspectives are also outlined.
Original languageEnglish
Article number595
Number of pages22
JournalFractal and Fractional
Issue number8
Publication statusPublished - 1 Aug 2023


  • Mathematical Oncology
  • computational modelling
  • Fractional Calculus
  • cancer
  • systems biology


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