Recent developments of Lyapunov-type inequalities for fractional differential equations

TL;DR

This paper surveys recent advances in Lyapunov-type inequalities for various fractional differential equations, covering diverse boundary conditions, fractional derivatives, and applications to boundary value problems.

Contribution

It provides a comprehensive overview of Lyapunov inequalities across multiple fractional derivatives and boundary conditions, highlighting recent developments and broad applicability.

Findings

Extensive collection of Lyapunov inequalities for fractional differential equations.

Inclusion of various boundary conditions and fractional derivatives.

Application to boundary value problems with fractional operators.

Abstract

A survey of results on Lyapunov-type inequalities for fractional differential equations associated with a variety of boundary conditions is presented. This includes Dirichlet, mixed, Robin, fractional, Sturm-Liouville, integral, nonlocal, multi-point, anti-periodic, conjugate, right-focal and impulsive conditions. Furthermore, our study includes Riemann-Liouville, Caputo, Hadamard, Prabhakar, Hilfer and conformable type fractional derivatives. Results for boundary value problems involving fractional $p$-Laplacian, fractional operators with nonsingular Mittag-Leffler kernels, $q$-difference, discrete, and impulsive equations, are also taken into account.