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

Jehad Alzabut (), Raghupathi Dhineshbabu, Abdelkader Moumen, A. George Maria Selvam and Mutti-Ur Rehman
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Jehad Alzabut: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Raghupathi Dhineshbabu: Department of Science and Humanities, R.M.K. College of Engineering and Technology (Autonomous), Puduvoyal, Thiruvallur 601 206, Tamil Nadu, India
Abdelkader Moumen: Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
A. George Maria Selvam: Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur 635 601, Tamil Nadu, India
Mutti-Ur Rehman: Center of Research and Innovation, Asia International University, Yangiobod MFY, G‘ijduvon Street, House 74, Bukhara 200100, Uzbekistan

Mathematics, 2024, vol. 13, issue 1, 1-15

Abstract: 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.

Keywords: discrete fractional calculus; boundary value problems; Ulam stability; Lyapunov inequality; eigenvalue problem; vertical column; rotating string (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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