Solvability for a Differential System of Duffing Type Via Caputo-Hadamard Approach

Authors

Mohamed BEZZIOU, UDBKM University and Laboratory LPAM of Mathematics, UMAB University of Mostaganem, AlgeriaFollow
Zoubir DAHMANI, Laboratory LMPA, Faculty of Exact Sciences and Informatics, University of Mostaganem, AlgeriaFollow
Iqbal JEBRIL, Department of Mathematics, Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, P.O. Box 130 Amman 11733, JordanFollow
Meriem Mansouria BELHAMITI, Laboratory LMPA, Faculty of Exact Sciences and Informatics, University of Mostaganem, AlgeriaFollow

Author Country (or Countries)

Algeria

Abstract

In this work, we investigate a new sequential coupled differential system of Duffing type. The considered system involves Caputo Hadamard derivatives. Based on both Banach contraction principle and Scheafer fixed point theorems, we establish two results on the existence and uniqueness of solutions for the introduced problem. Some examples are presented to show the validity of our results. To give more interpretation to the examples, we establish a new approximation of Caputo-Hadamard derivative for the case 1 < β < 2. Then, we plot the dynamics of one of the examples in terms of time and space coordinates.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/160222

Recommended Citation

BEZZIOU, Mohamed; DAHMANI, Zoubir; JEBRIL, Iqbal; and Mansouria BELHAMITI, Meriem (2022) "Solvability for a Differential System of Duffing Type Via Caputo-Hadamard Approach," Applied Mathematics & Information Sciences: Vol. 16: Iss. 2, Article 22.
DOI: http://dx.doi.org/10.18576/amis/160222
Available at: https://digitalcommons.aaru.edu.jo/amis/vol16/iss2/22