A study on variable-order delay fractional differential equations: existence, uniqueness, and numerical simulation via a predictor corrector algorithm
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Published:2024-06-05
Issue:7
Volume:99
Page:075211
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ISSN:0031-8949
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Container-title:Physica Scripta
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language:
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Short-container-title:Phys. Scr.
Author:
Rabhi Lahcene,
Zerari Amina,
Odibat ZaidORCID,
Shawagfeh Nabil
Abstract
Abstract
In this study, we adapted a predictor-corrector technique to simulate delay differential equations incorporating variable-order Caputo-type fractional derivatives. We addressed the existence and uniqueness of solutions for the studied models. Then, we presented numerical simulation of some delay differential equations with variable-order fractional derivatives to demonstrate the efficiency of the used technique. Various periodic and chaotic characteristics of the studied models are observed for some variable-orders from the performed graphical simulations. The used technique can be modified and extended to handle different classes of initial value problems which involve variable-order fractional derivatives.
Reference50 articles.
1. Fractional dynamics: applications of fractional calculus to dynamics of particles;Tarasov,2011