Sougata Dhar, Qingkai Kong
We study linear fractional boundary value problems consisting of an -th order Riemann-Liouville fractional differential equation with 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
|Qingkai Kong |
Department of Mathematics
Northern Illinois University
DeKalb, IL 60115, USA
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