LYAPUNOV TYPE INEQUALITIES AND THEIR APPLICATIONS ON AN EIGENVALUE PROBLEM FOR DISCRETE FRACTIONAL ORDER EQUATION WITH A CLASS OF BOUNDARY CONDITIONS

D. AbrahamVianny; R. Dhineshbabu; A. Selvam

D. AbrahamVianny Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635 601, Tamil Nadu, India
R. Dhineshbabu Department of Mathematics, Sir Venkateswara College of Engineering and Technology (Autonomous), Chittoor-517 127, Andhra Pradesh, India
A. Selvam Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635 601, Tamil Nadu, India

Article ID: 2570

Keywords: discrete fractional calculus; Lyapunov inequality; Green’s function; eigenvalue problem

Abstract

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

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