Lyapunov type inequalities for mixed nonlinear Riemann–Liouville fractional differential equations with a forcing term

摘要

In this paper, we present some new Lyapunov and Hartman type inequalities for Riemann–Liouville fractional differential equations of the form (aDαx)(t)+p(t)∣x(t)∣μ−1x(t)+q(t)∣x(t)∣γ−1x(t)=f(t), where p, q, f are real-valued functions and 0<γ<1<μ<2. No sign restrictions are imposed on the potential functions p, q and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.