On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative

On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative

In our research article, the mathematical model of fractional non-linear cancer dynamical system with the interaction of tumor cells, immune, and drugs reaction systems is taken in ABC derivative sense of fractional order. Qualitative results including existence and uniqueness has been analyzed by a...

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Main Authors: Muhammad Arfan, Kamal Shah, Aman Ullah, Meshal Shutaywi, Poom Kumam, Zahir Shah
Format: Article
Language:English
Published: Elsevier 2021-02-01
Series:Results in Physics
Subjects:
Fixed point approach
(AB) method
Numerical solution
Tumor cells
ABC derivative
Online Access:http://www.sciencedirect.com/science/article/pii/S2211379720321926
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spelling doaj-5b0f07a362334362937e2a4435d977912021-02-13T04:24:15ZengElsevierResults in Physics2211-37972021-02-0121103783On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivativeMuhammad Arfan0Kamal Shah1Aman Ullah2Meshal Shutaywi3Poom Kumam4Zahir Shah5Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, PakistanDepartment of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, PakistanDepartment of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, PakistanDepartment of Mathematics, College of Science & Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi ArabiaKMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan; Corresponding author at: KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand.Department of Mathematics, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa Pakistan; Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandIn our research article, the mathematical model of fractional non-linear cancer dynamical system with the interaction of tumor cells, immune, and drugs reaction systems is taken in ABC derivative sense of fractional order. Qualitative results including existence and uniqueness has been analyzed by applying some theorems of fixed point theory. The approximate results for the considered system are obtained by numerical method due to Adams–Bashforth (AB) in non-integer order. Simulation of the Obtained iterative scheme are then drawn against the real data for different non-integer order. The suitability of the proposed model for our results are applied to study dynamics of tumor cells which help in investigating the dynamical interaction among tumor cells, immune cells and drugs reaction of the disease.http://www.sciencedirect.com/science/article/pii/S2211379720321926Fixed point approach(AB) methodNumerical solutionTumor cellsABC derivative
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Arfan
Kamal Shah
Aman Ullah
Meshal Shutaywi
Poom Kumam
Zahir Shah
spellingShingle Muhammad Arfan
Kamal Shah
Aman Ullah
Meshal Shutaywi
Poom Kumam
Zahir Shah
On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative
Results in Physics
Fixed point approach
(AB) method
Numerical solution
Tumor cells
ABC derivative
author_facet Muhammad Arfan
Kamal Shah
Aman Ullah
Meshal Shutaywi
Poom Kumam
Zahir Shah
author_sort Muhammad Arfan
title On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative
title_short On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative
title_full On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative
title_fullStr On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative
title_full_unstemmed On fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative
title_sort on fractional order model of tumor dynamics with drug interventions under nonlocal fractional derivative
publisher Elsevier
series Results in Physics
issn 2211-3797
publishDate 2021-02-01
description In our research article, the mathematical model of fractional non-linear cancer dynamical system with the interaction of tumor cells, immune, and drugs reaction systems is taken in ABC derivative sense of fractional order. Qualitative results including existence and uniqueness has been analyzed by applying some theorems of fixed point theory. The approximate results for the considered system are obtained by numerical method due to Adams–Bashforth (AB) in non-integer order. Simulation of the Obtained iterative scheme are then drawn against the real data for different non-integer order. The suitability of the proposed model for our results are applied to study dynamics of tumor cells which help in investigating the dynamical interaction among tumor cells, immune cells and drugs reaction of the disease.
topic Fixed point approach
(AB) method
Numerical solution
Tumor cells
ABC derivative
url http://www.sciencedirect.com/science/article/pii/S2211379720321926
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