Lyapunov-type inequalities for fractional quasilinear problems via variational methods

In this paper, by variational methods, some Lyapunov-type inequalities are established for fractional quasilinear problems involving left and right Riemann-Liouville fractional derivative operators. To the authors’ knowledge, this is the first work, where Lyapunov-type inequalities for fractional boundary value problems are investigated by using variational methods. As an application of the obtained inequalities, we extend the notion of generalized eigenvalues to a fractional quasilinear system, and we derive some geometric properties of the fractional generalized spectrum.