Lyapunov type inequalities for the Riemann-Liouville fractional differential equations of higher order

摘要

In this paper, some new Lyapunov type inequalities will be presented for Riemann-Liouville fractional differential equations of the form ( D a α x ) ( t ) + p ( t ) | x ( t ) | μ − 1 x ( t ) + q ( t ) | x ( t ) | γ − 1 ( t ) x ( t ) = f ( t ) , $$igl(D^{lpha}_{a}xigr) (t)+p(t)ig| x(t)ig|^{mu-1}x (t)+q(t)ig| x(t)ig|^{gamma -1}(t)x(t)=f(t), $$ where α ∈ ( n − 1 , n ] $lphain(n-1, n]$ ( n ≥ 3 $ngeq3$ ), p, q, f are real-valued functions and 0 γ 1 μ n $0gamma1mun$ .