HIGHER ORDER NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

Khan, Rahmat Ali

• 투고 : 2011.08.26
• 발행 : 2014.03.31
• 16 4

초록

In this paper, we study the method of upper and lower solutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differential equations of the type $$^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)$$ $$u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})$$, where, n-1 < q < n, $n({\geq}3){\in}\mathbb{N}$, 0 < ${\eta},{\gamma},{\delta}$ < 1 and $^c\mathcal{D}^q_{0+}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.

키워드

boundary value problems;fractional differential equations;three-point boundary conditions;upper and lower solutions;generalized quasilinearization

참고문헌

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