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Application of the Caputo‐Fabrizio and Atangana‐Baleanu fractional derivatives to mathematical model of cancer chemotherapy effect

Application of the Caputo‐Fabrizio and Atangana‐Baleanu fractional derivatives to mathematical... In this paper, we obtain approximate‐analytical solutions of a cancer chemotherapy effect model involving fractional derivatives with exponential kernel and with general Mittag‐Leffler function. Laplace homotopy perturbation method and the modified homotopy analysis transform method were applied. The first method is based on a combination of the Laplace transform and homotopy methods, while the second method is an analytical technique based on homotopy polynomial. The cancer chemotherapy effect equations are solved numerically and analytically using the aforesaid methods. Illustrative examples are included to demonstrate the validity and applicability of the presented technique with new fractional‐order derivatives with exponential decay law and with general Mittag‐Leffler law. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Methods in the Applied Sciences Wiley

Application of the Caputo‐Fabrizio and Atangana‐Baleanu fractional derivatives to mathematical model of cancer chemotherapy effect

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References (69)

Publisher
Wiley
Copyright
© 2019 John Wiley & Sons, Ltd.
ISSN
0170-4214
eISSN
1099-1476
DOI
10.1002/mma.5421
Publisher site
See Article on Publisher Site

Abstract

In this paper, we obtain approximate‐analytical solutions of a cancer chemotherapy effect model involving fractional derivatives with exponential kernel and with general Mittag‐Leffler function. Laplace homotopy perturbation method and the modified homotopy analysis transform method were applied. The first method is based on a combination of the Laplace transform and homotopy methods, while the second method is an analytical technique based on homotopy polynomial. The cancer chemotherapy effect equations are solved numerically and analytically using the aforesaid methods. Illustrative examples are included to demonstrate the validity and applicability of the presented technique with new fractional‐order derivatives with exponential decay law and with general Mittag‐Leffler law.

Journal

Mathematical Methods in the Applied SciencesWiley

Published: Mar 15, 2020

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