Sougata Dhar, Qingkai Kong
Abstract:
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 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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