Unique positive solution for a fractional boundary value problem
2013 ◽
Vol 16
(4)
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Keyword(s):
AbstractIn this work we consider the unique positive solution for the following fractional boundary value problem $\left\{ \begin{gathered} D_{0 + }^\alpha u(t) = - f(t,u(t)),t \in [0,1], \hfill \\ u(0) = u'(0) = u'(1) = 0. \hfill \\ \end{gathered} \right. $ Here α ∈ (2, 3] is a real number, D 0+α is the standard Riemann-Liouville fractional derivative of order α. By using the method of upper and lower solutions and monotone iterative technique, we also obtain that there exists a sequence of iterations uniformly converges to the unique solution.
1991 ◽
Vol 162
(2)
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pp. 482-493
1989 ◽
Vol 13
(12)
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pp. 1399-1407
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2010 ◽
Vol 51
(9-10)
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pp. 1260-1267
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1992 ◽
Vol 5
(2)
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pp. 157-165
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