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Existence and Uniqueness of Solutions and Lyapunov-type Inequality for a Mixed Fractional Boundary Value Problem
  
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KeyWord:Fractional derivative; Lyapunov-type inequality; Fixed point theorem
Author NameAffiliation
Yani Liu School of Mathematical Sciences, Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Normal University, Shijiazhuang, Hebei 050024, China 
Qiaoluan Li School of Mathematical Sciences, Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Normal University, Shijiazhuang, Hebei 050024, China 
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Abstract:
      In this paper, a Lyapunov-type inequality for a linear differential equation involving right Riemann-Liouville and left Caputo fractional derivatives under Sturm-Liouville boundary conditions is established. Furthermore, the existence of solutions for the corresponding nonlinear differential equation is obtained by fixed point theorems.