Qualitative Analysis of a Three-Dimensional Dynamical System of Fractal-Fractional-Order Evolution Differential Equations with Terminal Boundary Conditions
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 and Banach’s fixed-point theorems, respectively. Ad...
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MDPI AG
2025-04-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/4/259 |
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| author | F. Gassem Arshad Ali Khaled Aldwoah Ria H. Egami Osman Osman Bakri Younis Amel Touati |
| author_facet | F. Gassem Arshad Ali Khaled Aldwoah Ria H. Egami Osman Osman Bakri Younis Amel Touati |
| author_sort | F. Gassem |
| collection | DOAJ |
| description | 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 and Banach’s fixed-point theorems, respectively. Additionally, the Hyers–Ulam stability approach is employed to analyze the system’s stability. We employ vector terminology for the proposed problem to make the analysis simple. To illustrate the practical relevance of our findings, we apply the derived results to a numerical example and graphically illustrate the solution for different fractal-fractional orders, emphasizing the effect of the derivative’s order on system behavior. |
| format | Article |
| id | doaj-art-9a1a63e80d054cccae07c496a8472d92 |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-9a1a63e80d054cccae07c496a8472d922025-08-20T02:18:11ZengMDPI AGFractal and Fractional2504-31102025-04-019425910.3390/fractalfract9040259Qualitative Analysis of a Three-Dimensional Dynamical System of Fractal-Fractional-Order Evolution Differential Equations with Terminal Boundary ConditionsF. Gassem0Arshad Ali1Khaled Aldwoah2Ria H. Egami3Osman Osman4Bakri Younis5Amel Touati6Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi ArabiaDepartment of Mathematics, University of Malakand, Chakdara 18000, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi ArabiaDepartment of Mathematics, College of Science and Humanity, Prince Sattam bin Abdulaziz University, Sulail, Al-Kharj 11942, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Mathematics, Faculty of Arts and Science, Elmagarda, King Khalid University, Abha 61421, Saudi ArabiaMathematics Department, College of Science, Northern Border University, Arar 91431, Saudi ArabiaIn 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 and Banach’s fixed-point theorems, respectively. Additionally, the Hyers–Ulam stability approach is employed to analyze the system’s stability. We employ vector terminology for the proposed problem to make the analysis simple. To illustrate the practical relevance of our findings, we apply the derived results to a numerical example and graphically illustrate the solution for different fractal-fractional orders, emphasizing the effect of the derivative’s order on system behavior.https://www.mdpi.com/2504-3110/9/4/259three-dimensional systemterminal boundary value problemsevolution differential equationsfixed-point resultsstability analysisfractional derivatives |
| spellingShingle | F. Gassem Arshad Ali Khaled Aldwoah Ria H. Egami Osman Osman Bakri Younis Amel Touati Qualitative Analysis of a Three-Dimensional Dynamical System of Fractal-Fractional-Order Evolution Differential Equations with Terminal Boundary Conditions Fractal and Fractional three-dimensional system terminal boundary value problems evolution differential equations fixed-point results stability analysis fractional derivatives |
| title | Qualitative Analysis of a Three-Dimensional Dynamical System of Fractal-Fractional-Order Evolution Differential Equations with Terminal Boundary Conditions |
| title_full | Qualitative Analysis of a Three-Dimensional Dynamical System of Fractal-Fractional-Order Evolution Differential Equations with Terminal Boundary Conditions |
| title_fullStr | Qualitative Analysis of a Three-Dimensional Dynamical System of Fractal-Fractional-Order Evolution Differential Equations with Terminal Boundary Conditions |
| title_full_unstemmed | Qualitative Analysis of a Three-Dimensional Dynamical System of Fractal-Fractional-Order Evolution Differential Equations with Terminal Boundary Conditions |
| title_short | Qualitative Analysis of a Three-Dimensional Dynamical System of Fractal-Fractional-Order Evolution Differential Equations with Terminal Boundary Conditions |
| title_sort | qualitative analysis of a three dimensional dynamical system of fractal fractional order evolution differential equations with terminal boundary conditions |
| topic | three-dimensional system terminal boundary value problems evolution differential equations fixed-point results stability analysis fractional derivatives |
| url | https://www.mdpi.com/2504-3110/9/4/259 |
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