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

Fractal and Fractional, Год журнала: 2025, Номер 9(2), С. 104 - 104

Опубликована: Фев. 8, 2025

This paper presents a novel framework for modeling nonlinear fractional evolution control systems. utilizes power non-local derivative (PFD), which is generalized that unifies several well-known derivatives, including Caputo–Fabrizio, Atangana–Baleanu, and Hattaf as special cases. It uniquely features tunable parameter “p”, providing enhanced over the representation of memory effects compared to traditional derivatives with fixed kernels. Utilizing fixed-point theory, we rigorously establish existence uniqueness solutions these systems under appropriate conditions. Furthermore, prove Hyers–Ulam stability system, demonstrating its robustness against small perturbations. We complement this practical numerical scheme based on Lagrange interpolation polynomials, enabling efficient computation solutions. Examples illustrating model’s applicability, symmetric cases, are supported by graphical representations highlight approach’s versatility. These findings address significant gap in literature pave way further research calculus diverse applications.

Язык: Английский

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

Fractal and Fractional, Год журнала: 2024, Номер 8(11), С. 638 - 638

Опубликована: Окт. 29, 2024

In this paper, we study human liver disease with a different approach of interval-based investigation by introducing subintervals. This may be referred to as short memory investigation. Such concepts are useful in problems where transition is observed when transitioning from one subinterval the other one. We use classical and fractal-fractional-order derivative each subinterval. existence solutions using Banach’s Krasnoselskii’s fixed-point theorems. Their stability analyzed adopting Hyers–Ulam (H-U) approach. Also, extended Adams–Bashforth–Moulton (ABM) method, simulate results that visually present numerical for values.

Язык: Английский

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

Fractal and Fractional, Год журнала: 2024, Номер 8(12), С. 735 - 735

Опубликована: Дек. 13, 2024

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

Язык: Английский

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Exploring Impulsive and Delay Differential Systems Using Piecewise Fractional Derivatives

Fractal and Fractional, Год журнала: 2025, Номер 9(2), С. 105 - 105

Опубликована: Фев. 10, 2025

This paper investigates a general class of variable-kernel discrete delay differential equations (DDDEs) with integral boundary conditions and impulsive effects, analyzed using Caputo piecewise derivatives. We establish results for the existence uniqueness solutions, as well their stability. The at least one solution is proven Schaefer’s fixed-point theorem, while established via Banach’s theorem. Stability examined through lens Ulam–Hyers (U-H) Finally, we illustrate application our theoretical findings numerical example.

Язык: Английский

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On a Certain Class of GA-Convex Functions and Their Milne-Type Hadamard Fractional-Integral Inequalities

Fractal and Fractional, Год журнала: 2025, Номер 9(2), С. 129 - 129

Опубликована: Фев. 19, 2025

In this article, we prove a new Milne-type inequality involving Hadamard fractional integrals for functions with GA-convex first derivatives. The limits of the error estimates involve incomplete gamma and confluent hypergeometric functions. results study open door to further investigation subject, as well extensions other forms generalized convexity, weighted formulas, higher dimensions.

Язык: Английский

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Investigation of fractional order model for glucose-insulin monitoring with PID and controllability

Scientific Reports, Год журнала: 2025, Номер 15(1)

Опубликована: Март 8, 2025

The global prevalence of diabetes, a chronic condition that disrupts glucose homeostasis, is rapidly increasing. Patients with diabetes face heightened challenges due to the COVID-19 pandemic, which exacerbates symptoms associated severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. In this study, we developed mathematical model utilizing Mittag–Leffler kernel in conjunction generalized fractal fractional operator explore complex dynamics progression and control. This effectively captures disease's inherent memory effects delayed responses, demonstrating improved accuracy over traditional integer-order models. We identified single equilibrium point represents stable level healthy individuals. To establish existence uniqueness model, employed fixed theory alongside Lipschitz condition. Ulam–Hyers stability proposed was also examined. Subsequently, analyzed chaotic behavior diabetic using feedback control approaches, focusing on controllability PID techniques. application chaos revealed glucose-insulin are highly sensitive initial conditions, leading oscillatory can result unstable levels. By implementing fractional-order controllers, stabilized dynamics, achieving more reliable blood sugar regulation compared conventional methods, notable reduction oscillation amplitude. conducted numerical simulations validate our findings, employing Newton polynomial method across various order values assess robustness results. A discussion graphical outcomes from simulations, MATLAB version 18, provided, illustrating under different fractal-fractional orders. comprehensive approach enhances understanding underlying mechanics driving dynamics.

Язык: Английский

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Fractional order modeling of prostate cancer with pulsed treatment and the impact of effector cell killing and cell competition

Scientific Reports, Год журнала: 2025, Номер 15(1)

Опубликована: Апрель 12, 2025

This manuscript illustrates a fractional-order mathematical model for prostate cancer (PC) growth under pulsed treatment, incorporating the effects of effector cell killing and competition between androgen-dependent (AD) androgen-independent (AI) PC cells. We establish existence uniqueness solutions using fixed-point theorems (Leray-Schauder Banach) investigate Ulam-Hyers stability to assess model's solution fractional order. Numerical results are obtained via Euler method simulation at various orders. Graphical illustrate dynamics, impact key parameters, including rate inter-cell competition, is investigated. These findings provide insights into complex interplay immune response, potentially informing therapeutic strategies PC.

Язык: Английский

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Theoretical and Numerical Analysis of the SIR Model and Its Symmetric Cases with Power Caputo Fractional Derivative

Fractal and Fractional, Год журнала: 2025, Номер 9(4), С. 251 - 251

Опубликована: Апрель 15, 2025

This paper introduces a novel fractional Susceptible-Infected-Recovered (SIR) model that incorporates power Caputo derivative (PCFD) and density-dependent recovery rate. enhances the model’s ability to capture memory effects represent realistic healthcare system dynamics in epidemic modeling. The utility flexibility are demonstrated through an application using parameters representative of COVID-19 pandemic. Unlike existing SIR models often limited representing diverse adequately, proposed PCFD framework encompasses extends well-known cases, such as those Caputo–Fabrizio Atangana–Baleanu derivatives. We prove our yields bounded positive solutions, ensuring biological plausibility. A rigorous analysis is conducted determine local stability, including derivation basic reproduction number (R0) sensitivity quantifying impact on R0. uniqueness existence solutions guaranteed via recursive sequence approach Banach fixed-point theorem. Numerical simulations, facilitated by numerical scheme applied parameter set, demonstrate varying order significantly alters predicted peak timing severity. Comparisons across different approaches highlight crucial role capacity shaping trajectories. These findings underscore potential generalized provide more nuanced potentially accurate predictions for disease outbreaks like COVID-19, thereby informing effective public health interventions.

Язык: Английский

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Qualitative Analysis of a Three-Dimensional Dynamical System of Fractal-Fractional-Order Evolution Differential Equations with Terminal Boundary Conditions

Fractal and Fractional, Год журнала: 2025, Номер 9(4), С. 259 - 259

Опубликована: Апрель 18, 2025

In this research article, we investigate a three-dimensional dynamical system governed by fractal-fractional-order evolution differential equations subject to terminal boundary conditions. We derive existence and uniqueness results using Schaefer’s Banach’s fixed-point theorems, respectively. Additionally, the Hyers–Ulam stability approach is employed analyze system’s stability. employ vector terminology for proposed problem make analysis simple. To illustrate practical relevance of our findings, apply derived numerical example graphically solution different fractal-fractional orders, emphasizing effect derivative’s order on behavior.

Язык: Английский

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Solutions behavior of mechanical oscillator equations with impulsive effects under Power Caputo fractional operator and its symmetric cases

Scientific Reports, Год журнала: 2025, Номер 15(1)

Опубликована: Май 9, 2025

Язык: Английский

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