An overview of mathematical modelling in cancer research: fractional calculus as modelling tool

LC Vieira, RS Costa, D Valério - Fractal and Fractional, 2023 - mdpi.com
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 …

A fractional modeling of tumor–immune system interaction related to lung cancer with real data

F Özköse, S Yılmaz, M Yavuz, İ Öztürk… - The European Physical …, 2022 - Springer
In this study, we investigate a new fractional-order mathematical model which considers
population dynamics among tumor cells-macrophage cells-active macrophage cells, and …

Fractional mathematical oncology: On the potential of non-integer order calculus applied to interdisciplinary models

CA Valentim, JA Rabi, SA David - Biosystems, 2021 - Elsevier
Mathematical Oncology investigates cancer-related phenomena through mathematical
models as comprehensive as possible. Accordingly, an interdisciplinary approach involving …

An optimization technique for solving a class of nonlinear fractional optimal control problems: application in cancer treatment

H Hassani, JAT Machado, S Mehrabi - Applied Mathematical Modelling, 2021 - Elsevier
This paper proposes an optimization method for solving a general form of nonlinear
fractional optimal control problems (NFOCP) governed by nonlinear fractional dynamical …

Qualitative analysis and numerical simulations of new model describing cancer

E Uçar, N Özdemir, E Altun - Journal of Computational and Applied …, 2023 - Elsevier
Cancer is a major illness which still results in the loss of human lives regardless of the
inroads we make in the scientific and medical world. For this reason, recently, the medical …

Can fractional calculus help improve tumor growth models?

CA Valentim Jr, NA Oliveira, JA Rabi… - Journal of Computational …, 2020 - Elsevier
ODE-based population models remain viable tools to investigate tumor growth and support
clinical evidence. By following a fractional approach, this study derives analytical solutions …

On multistep tumor growth models of fractional variable-order

CA Valentim, JA Rabi, SA David, JAT Machado - Biosystems, 2021 - Elsevier
Fractional mathematical oncology is a research topic that applies non-integer order calculus
to tackle cancer problems such as tumor growth analysis or its optimal treatment. This work …

Mathematical Modeling of Breast Cancer Based on the Caputo–Fabrizio Fractal-Fractional Derivative

M Idrees, AS Alnahdi, MB Jeelani - Fractal and Fractional, 2023 - mdpi.com
Breast cancer ranks among the most prevalent malignancies affecting the female population
and is a prominent contributor to cancer-related mortality. Mathematical modeling is a …

Fractional type multivariate neural network operators

U Kadak - Mathematical Methods in the Applied Sciences, 2023 - Wiley Online Library
In this paper, we introduce a novel family of multivariate neural network operators involving
Riemann‐Liouville fractional integral operator of order α. Their pointwise and uniform …

New fractional cancer mathematical model via IL-10 cytokine and anti-PD-L1 inhibitor

E Uçar, N Özdemir - Fractal and Fractional, 2023 - mdpi.com
In this study, we explore a recent biological model created to analyze the behavior of cancer
cells by administering a dose of a drug containing anti-PD-L1 and IL-10 with the Caputo and …