Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 95, pp. 19.
An extension of the LaxMilgram theorem and its
application to fractional differential equations
Nemat Nyamoradi, Mohammad Rassol Hamidi
Abstract:
In this article, using an iterative technique, we introduce an
extension of the LaxMilgram theorem which can be used for proving
the existence of solutions to boundaryvalue problems.
Also, we apply of the obtained result to the
fractional differential equation
where
and
are the right and
left RiemannLiouville fractional derivative of order
respectively,
is a parameter and
is a continuous function. Applying a regularity argument to this
equation, we show that every weak solution is a classical solution.
Submitted February 1, 2015. Published April 13, 2015.
Math Subject Classifications: 34A08, 35A15, 35B38.
Key Words: LaxMilgram theorem; fractional differential equation.
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Nemat Nyamoradi
Department of Mathematics, Faculty of Sciences
Razi University, 67149 Kermanshah, Iran
email: nyamoradi@razi.ac.ir, neamat80@yahoo.com


Mohammad Rassol Hamidi
Department of Mathematics, Faculty of Sciences
Razi University, 67149 Kermanshah, Iran
email: mohammadrassol.hamidi@yahoo.com

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