Highly accurate technique for studying some chaotic models described by ABC-fractional differential equations of variable-order

M. M. Khader and Ibrahim Al-Dayel
Additional contact information
M. M. Khader: Department of Mathematics and Statistics, College of Science, Imam Mohammad, Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia†Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
Ibrahim Al-Dayel: Department of Mathematics and Statistics, College of Science, Imam Mohammad, Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

International Journal of Modern Physics C (IJMPC), 2021, vol. 32, issue 02, 1-9

Abstract: The propose of this paper is to introduce and investigate a highly accurate technique for solving the fractional Logistic and Ricatti differential equations of variable-order. We consider these models with the most common nonsingular Atangana–Baleanu–Caputo (ABC) fractional derivative which depends on the Mittag–Leffler kernel. The proposed numerical technique is based upon the fundamental theorem of the fractional calculus as well as the Lagrange polynomial interpolation. We satisfy the efficiency and the accuracy of the given procedure; and study the effect of the variation of the fractional-order α(t) on the behavior of the solutions due to the presence of ABC-operator by evaluating the solution with different values of α(t). The results show that the given procedure is an easy and efficient tool to investigate the solution for such models. We compare the numerical solutions with the exact solution, thereby showing excellent agreement which we have found by applying the ABC-derivatives. We observe the chaotic solutions with some fractional-variable-order functions.

Keywords: Lagrange polynomial interpolation; Atangana–Baleanu–Caputo fractional derivative; Mittag–Leffer kernel; chaotic models; logistic and Riccati equations (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183121500182
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:32:y:2021:i:02:n:s0129183121500182

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183121500182

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().