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Analytical Solution of the Fractional Ro ̈ssler Chaotic System via a Novel Natural Transform Homotopy Method |
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PP: 179-189 |
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doi:10.18576/pfda/120112
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Author(s) |
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Ali Latif Arif,
Naser Rhaif Swain,
Hassan Kamil Jassim,
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Abstract |
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| This paper presents the development and application of a novel analytical technique, the Natural Transform Homotopy Perturbation Method (NTHPM), for obtaining approximate solutions to nonlinear fractional-order differential equations. The methodology is specifically formulated for systems incorporating the Atangana-Baleanu fractional operator, which possesses non-singular and non-local kernel properties. The primary objective is to employ this technique to derive an analytical approximate solution for the fractional-order Ro ̈ssler system, a canonical model of chaotic dynamics. Furthermore, the study rigorously establishes the existence and uniqueness of the solution for the considered fractional-order system under appropriate conditions, thereby providing a solid theoretical foundation for the applied method. The results demonstrate the efficacy and computational advantages of the proposed NTHPM in handling the complexity inherent in nonlinear fractional systems, offering a powerful tool for their analysis and simulation. |
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