Fractal-Fractional-Order Modeling of Liver Fibrosis Disease and Its Mathematical Results with Subinterval Transitions

Hamza, Amjad E.; Osman, Osman; Ali, Arshad; Alsulami, Amer; Aldwoah, Khaled; Mustafa, Alaa; Saber, Hicham

doi:10.3390/fractalfract8110638

Fractal Fract

2024

DOI: 10.3390/fractalfract8110638

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Fractal-Fractional-Order Modeling of Liver Fibrosis Disease and Its Mathematical Results with Subinterval Transitions

Amjad E. Hamza,

Osman Osman,

Arshad Ali

et al.

Abstract: In this paper, we study human liver disease with a different approach of interval-based investigation by introducing subintervals. This investigation may be referred to as a short memory investigation. Such concepts are useful in problems where a transition is observed when transitioning from one subinterval to the other one. We use the classical and fractal-fractional-order derivative in each subinterval. We study the existence of solutions by using Banach’s and Krasnoselskii’s fixed-point theorems. Their sta… Show more

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Cited by 2 publications

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Fixed Point and Stability Analysis of a Tripled System of Nonlinear Fractional Differential Equations with n-Nonlinear Terms

Algolam,

Osman,

Ali

et al. 2024

Fractal Fract

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This research article investigates a tripled system of nonlinear fractional differential equations with n terms. The study explores this novel class of differential equations to establish existence and stability results. Utilizing Schaefer’s and Banach’s fixed point theorems, we derive sufficient conditions for the existence of at least one solution, as well as a unique solution. Furthermore, we apply Hyers–Ulam stability analysis to establish criteria for the stability of the system. To demonstrate the applicability of the main results, a detailed example is provided.

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Fixed Point and Stability Analysis of a Tripled System of Nonlinear Fractional Differential Equations with n-Nonlinear Terms

Algolam,

Osman,

Ali

et al. 2024

Fractal Fract

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Investigating a Nonlinear Fractional Evolution Control Model Using W-Piecewise Hybrid Derivatives: An Application of a Breast Cancer Model

Saber,

Almalahi,

Albala

et al. 2024

Fractal Fract

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Many real-world phenomena exhibit multi-step behavior, demanding mathematical models capable of capturing complex interactions between distinct processes. While fractional-order models have been successfully applied to various systems, their inherent smoothness often limits their ability to accurately represent systems with discontinuous changes or abrupt transitions. This paper introduces a novel framework for analyzing nonlinear fractional evolution control systems using piecewise hybrid derivatives with respect to a nondecreasing function W(ι). Building upon the theoretical foundations of piecewise hybrid derivatives, we establish sufficient conditions for the existence, uniqueness, and Hyers–Ulam stability of solutions, leveraging topological degree theory and functional analysis. Our results significantly improve upon existing theoretical understanding by providing less restrictive conditions for stability compared with standard fixed-point theorems. Furthermore, we demonstrate the applicability of our framework through a simulation of breast cancer disease dynamics, illustrating the impact of piecewise hybrid derivatives on the model’s behavior and highlighting advantages over traditional modeling approaches that fail to capture the multi-step nature of the disease. This research provides robust modeling and analysis tools for systems exhibiting multi-step behavior across diverse fields, including engineering, physics, and biology.

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Fractal-Fractional-Order Modeling of Liver Fibrosis Disease and Its Mathematical Results with Subinterval Transitions

Cited by 2 publications

References 31 publications

Fixed Point and Stability Analysis of a Tripled System of Nonlinear Fractional Differential Equations with n-Nonlinear Terms

Fixed Point and Stability Analysis of a Tripled System of Nonlinear Fractional Differential Equations with n-Nonlinear Terms

Investigating a Nonlinear Fractional Evolution Control Model Using W-Piecewise Hybrid Derivatives: An Application of a Breast Cancer Model

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