Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 106, pp. 115.
Existence of solutions to boundary value problems arising
from the fractional advection dispersion equation
Lingju Kong
Abstract:
We study the existence of multiple solutions to the
boundary value problem
where
,
is a parameter,
,
and
are, respectively, the left and right RiemannLiouville
fractional integrals of order
,
is a given function.
Our interest in the above system arises from studying the steady fractional
advection dispersion equation.
By applying variational methods, we obtain sufficient conditions
under which the above equation has at least three solutions.
Our results are new even for the special case when
.
Examples are provided to illustrate the applicability of our results.
Submitted December 17, 2012. Published April 24, 2013.
Math Subject Classifications: 34B15, 34A08.
Key Words: Three solutions; fractional boundary value problem;
variational methods.
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Lingju Kong
Department of Mathematics
the University of Tennessee at Chattanooga
Chattanooga, TN 37403, USA
email: LingjuKong@utc.edu

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