Lyapunov-type inequalities for fractional differential equations: a survey

Abstract

A survey of results on Lyapunov-type inequalities for fractional differential equations associated with a variety of boundary conditions is presented. We have included some recent work on the topic dealing with sequential, Caputo-Fabrizio, Hadamard, Hilfer, Katugampola, hyprid, or nested fractional derivatives. We have also focused on Lyapunov-type inequalities for problems containing fractional derivatives with respect to a certain function, systems of fractional differential equations, and conformable derivatives. Furthermore, Lyapunov-type inequalities for fractional differential equations based on non Green function approach are discussed.

Keywords

• lyapunov-type inequality
• fractional derivative
• fractional integral
• green’s function
• fractional boundary value problem
• eigenvalue problem