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http://dx.doi.org/10.14317/jami.2013.221

THREE-POINT BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS  

Khan, Rahmat Ali (Department of Mathematics, University of Malakand)
Publication Information
Journal of applied mathematics & informatics / v.31, no.1_2, 2013 , pp. 221-228 More about this Journal
Abstract
The method of upper and lower solutions and the generalized quasilinearization technique is developed for the existence and approximation of solutions to boundary value problems for higher order fractional differential equations of the type $^c\mathcal{D}^qu(t)+f(t,u(t))=0$, $t{\in}(0,1),q{\in}(n-1,n],n{\geq}2$ $u^{\prime}(0)=0,u^{\prime\prime}(0)=0,{\ldots},u^{n-1}(0)=0,u(1)={\xi}u({\eta})$, where ${\xi},{\eta}{\in}(0,1)$, the nonlinear function f is assumed to be continuous and $^c\mathcal{D}^q$ is the fractional derivative in the sense of Caputo. Existence of solution is established via the upper and lower solutions method and approximation of solutions uses the generalized quasilinearization technique.
Keywords
Boundary value problems; Fractional differential equations; Three-point boundary conditions; Upper and lower solutions; Generalized quasilinearization;
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