Lyapunov-type inequalities for $\alpha$-th order fractional differential equations with 2<$\alpha\le3$ and fractional boundary conditions

• Main Authors: Sougata Dhar, Qingkai Kong
• Format: Article
• Language: English
• Published: Texas State University 2017-09-01
• Series: Electronic Journal of Differential Equations
• Subjects: Fractional differential equations; fractional boundary conditions; Lyapunov-type inequalities; boundary value problems; existence and uniqueness of solutions
• Online Access: http://ejde.math.txstate.edu/Volumes/2017/203/abstr.html
• ISSN: 1072-6691

We study linear fractional boundary value problems consisting of an $\alpha$-th order Riemann-Liouville fractional differential equation with 2<$\alpha\leq 3$ and certain fractional boundary conditions. We derive several Lyapunov-type inequalities and apply them to establish nonexistence, uniqueness, and existence-uniqueness of solutions for related homogeneous and nonhomogeneous linear fractional boundary value problems. As a special case, our work extends some existing results for third-order linear boundary value problems.