Perturbation results and monotone iterative technique for fractional evolution equations (Q638149)

Summary: We mainly study the fractional evolution equation in an ordered Banach space \(X^{C}D_{0}^{a} + u(t) + Au(t) = f(t, u(t), Gu(t))\), \(1 < {\alpha} < 2\), \(u(0) = x \in X\), \(u'(0) = \theta\). Using the monotone iterative technique based on lower and upper solutions, the existence and uniqueness results are obtained. The necessary perturbation results for accomplishing this approach are also developed.