HIGHER ORDER NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

Title & Authors
HIGHER ORDER NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS
Khan, Rahmat Ali;

Abstract
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 $\small{^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)}$ $\small{u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})}$, where, n-1 < q < n, $\small{n({\geq}3){\in}\mathbb{N}}$, 0 < $\small{{\eta},{\gamma},{\delta}}$ < 1 and $\small{^c\mathcal{D}^q_{0+}}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.
Keywords
boundary value problems;fractional differential equations;three-point boundary conditions;upper and lower solutions;generalized quasilinearization;
Language
English
Cited by
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