The Lyapunov inequality has its importance in the study of broad applications of solutions to differential and difference equations, such as oscillation theory, disconjugacy and eigenvalue problems. This paper is devoted to a new Lyapunov-type inequality for discrete fractional order equations with a class of two-point boundary conditions under the concept of the Riemann-Liouville fractional difference operator. We examine some new results for linear and nonlinear Lyapunov-type inequalities by developing suitable Green’s function and determining their corresponding maximum value for discrete fractional equations. The associated eigenvalue problem is also examined. We provide a couple of examples to demonstrate the applicability of the findings.

discrete fractional calculus, Lyapunov inequality, Green’s function, eigenvalue problem.

Received: January 30, 2022; Revised: April 11, 2022; Accepted: May 4, 2022; Published: June 4, 2022

How to cite this article: D. Abraham Vianny, R. Dhineshbabu and A. George Maria Selvam, Lyapunov type inequalities and their applications on an eigenvalue problem for discrete fractional order equation with a class of boundary conditions, Advances in Differential Equations and Control Processes 28 (2022), 55-71. http://dx.doi.org/10.17654/0974324322024

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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