Lyapunov type inequalities for mixed nonlinear Riemann-Liouville fractional differential equations with a forcing term
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文摘
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&minus;1x(t)+q(t)∣x(t)∣γ&minus;1x(t)=f(t),(aDαx)(t)+p(t)∣x(t)∣μ&minus;1x(t)+q(t)∣x(t)∣γ&minus;1x(t)=f(t), where pp, qq, ff are real-valued functions and 0<γ<1<μ<20<γ<1<μ<2. No sign restrictions are imposed on the potential functions pp, qq and the forcing term ff. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.
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