Browsing by Author "Erturk, Vedat Suat"

Now showing 1 - 2 of 2

Citation Count: 0
A comparative study for mathematical modelling of the contest of CAR-T and tumour cells in solid cancers using fractional- and integer-order derivatives
(Springernature, 2024) Kumar, Pushpendra; Erturk, Vedat Suat
Cancer is a disease resulting from the fractious growth and division of abnormal cells and has gotten consistent and dedicated attention from scientists across multiple disciplines. To date, several mathematical studies have been done to study its dynamics. In this paper, we study two fractional-order mathematical models that describe the competition between CAR-T and tumour cells in terms of their immune-suppressive efficiency. We explore whether the use of a large number of CAR-T cells encountering the antigens of solid tumours could beat the immune-suppressive force of cancer. Our results are obtained through the implementation of the well-known Caputo fractional derivative as well as the Adams-Bashforth-Moulton scheme. The main aim of this study is to compare the results we obtained through the use of fractional derivatives with previously published integer-order simulations. Of interest are the instances when the results obtained via the fractional-order derivative contradict the solutions provided by the integer-order models.
Citation Count: 0
A variable-order fractional mathematical model for the strategy to combat the atmospheric level of carbon dioxide
(Springer Heidelberg, 2024) Kumar, Pushpendra; Erturk, Vedat Suat
In this article, we define a nonlinear model for exploring the strategy of combating the atmospheric level of carbon dioxide (CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}) considering development activities in terms of variable-order Liouville-Caputo fractional derivatives. There are two types of variable-order Liouville-Caputo fractional derivatives used to derive the proposed model. We prove the existence and uniqueness of the solution for the given model using fixed-point theory. The numerical solution is derived by using a recently proposed predictor-corrector scheme. We perform several graphical simulations to describe the outcomes of the given model. The outputs performed at various fractional-order values provide novel findings to understand how to combat atmospheric CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}. A novel variable-order fractional model that captures memory effects in the proposed dynamics, along with a recent numerical methodology, are the key features of this study. The simulation analysis shows that the leafy tree plantation on the excess land will be efficient against atmospheric CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}.