TY - JOUR
T1 - On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method
AU - Shah, Kamal
AU - Abdeljawad, Thabet
AU - Jarad, Fahd
AU - Al-Mdallal, Qasem
N1 - Funding Information:
Acknowledgement: The authors K. Shah and T. Abdeljawad would like to thank Prince Sultan University for the support through the TAS Research Lab.
Publisher Copyright:
© 2023 Tech Science Press. All rights reserved.
PY - 2023
Y1 - 2023
N2 - This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using Matlab-16, we simulate the series solution to illustrate our results graphically. Finally, a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.
AB - This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using Matlab-16, we simulate the series solution to illustrate our results graphically. Finally, a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.
KW - conformable fractional differential transform
KW - existence results
KW - Prey predator model
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U2 - 10.32604/cmes.2023.021523
DO - 10.32604/cmes.2023.021523
M3 - Article
AN - SCOPUS:85148238626
SN - 1526-1492
VL - 136
SP - 1457
EP - 1472
JO - CMES - Computer Modeling in Engineering and Sciences
JF - CMES - Computer Modeling in Engineering and Sciences
IS - 2
ER -