Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations

In this paper, we are concerned with the nonlinear differential equation of fractional order D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , 1 < α ≤ 2 , where D 0 + α is the standard Riemann–Liouville fractional order derivative, subject to the boundary conditions u ( 0 ) = 0 , D 0 +...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 59; no. 3; pp. 1363 - 1375
Main Authors Li, C.F., Luo, X.N., Zhou, Yong
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2010
Subjects
Boundary value problem
Carathéodory conditions
Fractional differential equation
Positive solution
Riemann–Liouville derivative
Fractional differential equation
Riemann–Liouville derivative
Boundary value problem
Carathéodory conditions
Positive solution
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Summary:In this paper, we are concerned with the nonlinear differential equation of fractional order D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , 1 < α ≤ 2 , where D 0 + α is the standard Riemann–Liouville fractional order derivative, subject to the boundary conditions u ( 0 ) = 0 , D 0 + β u ( 1 ) = a D 0 + β u ( ξ ) . We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2009.06.029