Ulam Stability, Lyapunov-Type Inequality, and the Eigenvalue Problem for Model of Discrete Fractional-Order Deflection Equations of Vertical Columns and a Rotating String with Two-Point Boundary Conditions
Due to its significance in numerous scientific and engineering domains, discrete fractional calculus (DFC) has received much attention recently. In particular, it seems that the exploration of the stability of DFC is crucial. A mathematical model of the discrete fractional equation describing the de...
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2024-12-01
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| Series: | Mathematics |
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| author | Jehad Alzabut Raghupathi Dhineshbabu Abdelkader Moumen A. George Maria Selvam Mutti-Ur Rehman |
| author_facet | Jehad Alzabut Raghupathi Dhineshbabu Abdelkader Moumen A. George Maria Selvam Mutti-Ur Rehman |
| author_sort | Jehad Alzabut |
| collection | DOAJ |
| description | Due to its significance in numerous scientific and engineering domains, discrete fractional calculus (DFC) has received much attention recently. In particular, it seems that the exploration of the stability of DFC is crucial. A mathematical model of the discrete fractional equation describing the deflection of a vertical column along with two-point boundary conditions featuring the Riemann–Liouville operator is constructed to study several kinds of Ulam stability results in this research work. In addition, we developed Lyapunov-type inequality and its application to an eigenvalue problem for discrete fractional rotating string equations. Finally, the effectiveness of the theoretical findings is demonstrated with numerical examples. |
| format | Article |
| id | doaj-art-a7fd30079519445a82cfb7489b69cce5 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-a7fd30079519445a82cfb7489b69cce52025-01-10T13:17:58ZengMDPI AGMathematics2227-73902024-12-011311810.3390/math13010018Ulam Stability, Lyapunov-Type Inequality, and the Eigenvalue Problem for Model of Discrete Fractional-Order Deflection Equations of Vertical Columns and a Rotating String with Two-Point Boundary ConditionsJehad Alzabut0Raghupathi Dhineshbabu1Abdelkader Moumen2A. George Maria Selvam3Mutti-Ur Rehman4Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Science and Humanities, R.M.K. College of Engineering and Technology (Autonomous), Puduvoyal, Thiruvallur 601 206, Tamil Nadu, IndiaDepartment of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi ArabiaDepartment of Mathematics, Sacred Heart College (Autonomous), Tirupattur 635 601, Tamil Nadu, IndiaCenter of Research and Innovation, Asia International University, Yangiobod MFY, G‘ijduvon Street, House 74, Bukhara 200100, UzbekistanDue to its significance in numerous scientific and engineering domains, discrete fractional calculus (DFC) has received much attention recently. In particular, it seems that the exploration of the stability of DFC is crucial. A mathematical model of the discrete fractional equation describing the deflection of a vertical column along with two-point boundary conditions featuring the Riemann–Liouville operator is constructed to study several kinds of Ulam stability results in this research work. In addition, we developed Lyapunov-type inequality and its application to an eigenvalue problem for discrete fractional rotating string equations. Finally, the effectiveness of the theoretical findings is demonstrated with numerical examples.https://www.mdpi.com/2227-7390/13/1/18discrete fractional calculusboundary value problemsUlam stabilityLyapunov inequalityeigenvalue problemvertical column |
| spellingShingle | Jehad Alzabut Raghupathi Dhineshbabu Abdelkader Moumen A. George Maria Selvam Mutti-Ur Rehman Ulam Stability, Lyapunov-Type Inequality, and the Eigenvalue Problem for Model of Discrete Fractional-Order Deflection Equations of Vertical Columns and a Rotating String with Two-Point Boundary Conditions Mathematics discrete fractional calculus boundary value problems Ulam stability Lyapunov inequality eigenvalue problem vertical column |
| title | Ulam Stability, Lyapunov-Type Inequality, and the Eigenvalue Problem for Model of Discrete Fractional-Order Deflection Equations of Vertical Columns and a Rotating String with Two-Point Boundary Conditions |
| title_full | Ulam Stability, Lyapunov-Type Inequality, and the Eigenvalue Problem for Model of Discrete Fractional-Order Deflection Equations of Vertical Columns and a Rotating String with Two-Point Boundary Conditions |
| title_fullStr | Ulam Stability, Lyapunov-Type Inequality, and the Eigenvalue Problem for Model of Discrete Fractional-Order Deflection Equations of Vertical Columns and a Rotating String with Two-Point Boundary Conditions |
| title_full_unstemmed | Ulam Stability, Lyapunov-Type Inequality, and the Eigenvalue Problem for Model of Discrete Fractional-Order Deflection Equations of Vertical Columns and a Rotating String with Two-Point Boundary Conditions |
| title_short | Ulam Stability, Lyapunov-Type Inequality, and the Eigenvalue Problem for Model of Discrete Fractional-Order Deflection Equations of Vertical Columns and a Rotating String with Two-Point Boundary Conditions |
| title_sort | ulam stability lyapunov type inequality and the eigenvalue problem for model of discrete fractional order deflection equations of vertical columns and a rotating string with two point boundary conditions |
| topic | discrete fractional calculus boundary value problems Ulam stability Lyapunov inequality eigenvalue problem vertical column |
| url | https://www.mdpi.com/2227-7390/13/1/18 |
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