Analyzing the stability of fractal delay differential equations

Alireza Khalili Golmankhaneh and Cemil Tunç

Chaos, Solitons & Fractals, 2024, vol. 188, issue C

Abstract: In this paper, we provide a comprehensive overview of fractal calculus and investigate the stability of both linear and non-linear fractal delay differential equations with fractal support. Our analysis encompasses the stability of the fractal Mackey–Glass equation as well as fractal differential equations with single and dual delays. Additionally, we introduce a predictor–corrector scheme to solve the fractal one-delay differential equation. Several examples are presented to illustrate the effects of fractal-order differentiation, which arise from the dimensionality of the fractal support, and the impact of fractal delays.

Keywords: Fractal calculus; Fractal delay differential; Stability of the fractal Mackey–Glass; Predictor–corrector scheme (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010440

DOI: 10.1016/j.chaos.2024.115492

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