ON NUMERICAL AND THEORETICAL FINDINGS FOR FRACTAL-FRACTIONAL ORDER GENERALIZED DYNAMICAL SYSTEM

Haidong Qu (), Muhammad Arfan (), Kamal Shah, Aman Ullah (), Thabet Abdeljawad and Gengzhong Zhang ()
Additional contact information
Haidong Qu: Department of Mathematics, Hanshan Normal University, Chaozhou 515041, P. R. China
Muhammad Arfan: Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
Kamal Shah: Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan†Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia
Aman Ullah: Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
Thabet Abdeljawad: ��Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia‡Department of Medical Research, China Medical University, Taichung 40402, Taiwan§Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea¶Department of Computer Science and Technology, Hanshan Normal University, ChaoZhou, Guangdong 521041, P. R. China
Gengzhong Zhang: �Department of Computer Science and Technology, Hanshan Normal University, ChaoZhou, Guangdong 521041, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 02, 1-19

Abstract: In this paper, we consider a general system of fractal-fractional order derivative in Atangana–Baleanu–Caputo sense. On the application of fixed point approach, we establish sufficient conditions regarding existence and uniqueness of solution. The said requirements are obtained via using Krasnoselkii’s and Banach fixed results. Further via nonlinear analysis, some interesting results for Hyers–Ulam (HU)-type stability are also derived. To compute numerical solution for the proposed nonlinear system, fractal-fractional order Adams–Bashforth method is used. To support our findings, we give some test problems. Also by Matlab, we also present their graphical interpretation. The analysis of this paper is in generalized format which can be applied to any real problem. Each equation is investigated separately for the said characteristics.

Keywords: General System; Fractal-Fractional Order Derivative; Fixed Point Approach; Fractional Order Adams–Bashforth Method (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X23400194
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:fracta:v:31:y:2023:i:02:n:s0218348x23400194

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X23400194

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().