Lyapunov-Type Inequality for a Riemann-Liouville Type Fractional Boundary Value Problem with Robin Boundary Conditions

TL;DR

This paper derives a Lyapunov-type inequality for Riemann-Liouville fractional boundary value problems with Robin conditions and uses it to determine when certain Mittag-Leffler functions have no real zeros.

Contribution

It introduces a new Lyapunov-type inequality specific to Riemann-Liouville fractional problems with Robin boundary conditions, expanding analytical tools in fractional calculus.

Findings

Established a Lyapunov-type inequality for fractional boundary value problems.

Provided a criterion for the nonexistence of real zeros of Mittag-Leffler functions.

Enhanced understanding of fractional boundary value problems with Robin conditions.

Abstract

In this article we establish a Lyapunov-type inequality for two-point Riemann-Liouville fractional boundary value problems associated with well-posed Robin boundary conditions. To illustrate the applicability of established result, we deduce criterion for the nonexistence of real zeros of a Mittag-Leffler function.