Fractional de la Vall\'ee Poussin inequalities

TL;DR

This paper extends the de la Vallée Poussin inequalities to fractional boundary value problems, providing new bounds and improving the understanding of zeros of Mittag-Leffler functions.

Contribution

It introduces generalized inequalities for fractional problems and refines zero-free intervals for Mittag-Leffler functions, advancing fractional analysis.

Findings

Derived generalized inequalities for fractional boundary value problems.

Improved zero-free intervals for Mittag-Leffler functions.

Enhanced understanding of fractional differential equations.

Abstract

In this work we derive some inequalities for fractional boundary value problems, that generalize the well-known de la Vall\'ee Poussin inequality. With our results we also were able to improve the intervals where some Mittag-Leffler functions don't possess real zeros.