The Stability and Global Attractivity of Fractional Differential Equations with the Ψ-Hilfer Derivative in the Context of an Economic Recession

The Stability and Global Attractivity of Fractional Differential Equations with the Ψ-Hilfer Derivative in the Context of an Economic Recession

Fractional differential equations (FDEs) are employed to describe the physical universe. This article investigates the attractivity of solutions for FDEs and Ulam–Hyers–Rassias stability, involving the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="...

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Bibliographic Details
Main Authors: Mdi Begum Jeelani, Farva Hafeez, Nouf Abdulrahman Alqahtani
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Fractal and Fractional
Subjects:
fractional differential equations (FDEs)
Ulam-Hyers-Rassias stability
Ψ-Hilfer rractional derivative
Krasnoselskii’s fixed point theorem
financial crisis model
Online Access:https://www.mdpi.com/2504-3110/9/2/113
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Summary:Fractional differential equations (FDEs) are employed to describe the physical universe. This article investigates the attractivity of solutions for FDEs and Ulam–Hyers–Rassias stability, involving the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ψ</mo></semantics></math></inline-formula>-Hilfer fractional derivative. Important results are presented using Krasnoselskii’s fixed point theorem, which provides a framework for analyzing the stability and attractivity of solutions. Novel results on the attractiveness of solutions to nonlinear FDEs in Banach spaces are derived, and the existence of solutions, stability properties, and behavior of system equilibria are examined. The application of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ψ</mo></semantics></math></inline-formula>-Hilfer fractional derivatives in modeling financial crises is explored, and a financial crisis model using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ψ</mo></semantics></math></inline-formula>-Hilfer fractional derivatives is proposed, providing more general and global results. Furthermore, we also perform a numerical analysis to validate our theoretical findings.
ISSN:2504-3110

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