Advances in Differential Equations and Control Processes

The Advances in Differential Equations and Control Processes is an esteemed international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research articles related to recent developments in both theory and applications of ordinary and partial differential equations, integral equations, and control theory. The journal highlights the interdisciplinary nature of these topics, with applications in physical, biological, environmental, and health sciences, mechanics, and engineering. It also considers survey articles that identify future avenues of advancement in the field.

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

Authors

  • D. Abraham Vianny
  • R. Dhineshbabu
  • A. George Maria Selvam

Keywords:

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

DOI:

https://doi.org/10.17654/0974324322024

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.

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

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Published

2022-06-04

Issue

Vol. 28 (2022)

Section

Articles

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How to Cite

LYAPUNOV TYPE INEQUALITIES AND THEIR APPLICATIONS ON AN EIGENVALUE PROBLEM FOR DISCRETE FRACTIONAL ORDER EQUATION WITH A CLASS OF BOUNDARY CONDITIONS. (2022). Advances in Differential Equations and Control Processes, 28, 55-71. https://doi.org/10.17654/0974324322024

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