Electron. J. Differential Equations, Vol. 2017 (2017), No. 203, pp. 1-15.

Lyapunov-type inequalities for $\alpha$-th order fractional differential equations with $2<\alpha\leq 3$ and fractional boundary conditions

Sougata Dhar, Qingkai Kong

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.

Submitted June 2, 2017. Published September 6, 2017.
Math Subject Classifications: 34A08, 34A40, 26A33, 34B05.
Key Words: Fractional differential equations; fractional boundary conditions; Lyapunov-type inequalities; boundary value problems; existence and uniqueness of solutions.

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Sougata Dhar
Department of Mathematics and Statistics
University of Maine
Orono, ME 04469, USA
email: sougata.dhar@maine.edu
Qingkai Kong
Department of Mathematics
Northern Illinois University
DeKalb, IL 60115, USA
email: qkong@niu.edu

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