Bulletin of the
Korean Mathematical Society BKMS

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 \begin{align*} {}^{c}&\mathcal{D}_{0+}^{q}u(t)+f(t,u(t))=0,\,t\in(0,1)\\ &u'(0)=\gamma u'(\eta),~ u''(0)=0,~ u'''(0)=0, \ldots, u^{(n-1)}(0)=0,\,u(1)=\delta u(\eta), \end{align*} where, $n-1

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

MSC numbers: 26A33, 34K05, 34K07