Nonlinear Fractional Evolution Control Modeling via Power Non-Local Kernels: A Generalization of Caputo–Fabrizio, Atangana–Baleanu, and Hattaf Derivatives

Nonlinear Fractional Evolution Control Modeling via Power Non-Local Kernels: A Generalization of Caputo–Fabrizio, Atangana–Baleanu, and Hattaf Derivatives

This paper presents a novel framework for modeling nonlinear fractional evolution control systems. This framework utilizes a power non-local fractional derivative (PFD), which is a generalized fractional derivative that unifies several well-known derivatives, including Caputo–Fabrizio, Atangana–Bale...

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Bibliographic Details
Main Authors: F. Gassem, Mohammed Almalahi, Osman Osman, Blgys Muflh, Khaled Aldwoah, Alwaleed Kamel, Nidal Eljaneid
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Fractal and Fractional
Subjects:
evolution systems
power non-local kernels
existence of solutions
Hyers–Ulam stability analysis
fractional derivatives
Online Access:https://www.mdpi.com/2504-3110/9/2/104
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Summary:This paper presents a novel framework for modeling nonlinear fractional evolution control systems. This framework utilizes a power non-local fractional derivative (PFD), which is a generalized fractional derivative that unifies several well-known derivatives, including Caputo–Fabrizio, Atangana–Baleanu, and generalized Hattaf derivatives, as special cases. It uniquely features a tunable power parameter “<i>p</i>”, providing enhanced control over the representation of memory effects compared to traditional derivatives with fixed kernels. Utilizing the fixed-point theory, we rigorously establish the existence and uniqueness of solutions for these systems under appropriate conditions. Furthermore, we prove the Hyers–Ulam stability of the system, demonstrating its robustness against small perturbations. We complement this framework with a practical numerical scheme based on Lagrange interpolation polynomials, enabling efficient computation of solutions. Examples illustrating the model’s applicability, including symmetric cases, are supported by graphical representations to highlight the approach’s versatility. These findings address a significant gap in the literature and pave the way for further research in fractional calculus and its diverse applications.
ISSN:2504-3110

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