University of Tabriz Computational Methods for Differential Equations 2345-3982 11 1 2023 01 01 Extremal solutions for multi-term nonlinear fractional differential equations with nonlinear boundary conditions 32 41 14147 10.22034/cmde.2021.48310.2018 EN Hossein Fazli Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran. Fariba Bahrami Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran. Sedaghat Shahmorad Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran. Journal Article 2021 10 07 This paper is devoted to prove the existence of extremal solutions for multi-term nonlinear fractional differential equations with nonlinear boundary conditions. The fractional derivative is of Caputo type and the inhomogeneous term depends on the fractional derivatives of lower orders. By establishing a new comparison theorem and applying the monotone iterative technique, we show the existence of extremal solutions. The method is a constructive method that yields monotone sequences that converge to the extremal solutions. As an application, some examples are presented to illustrate the main results. https://cmde.tabrizu.ac.ir/article_14147_bcdaf68ffaf4cb098ee1253cb5ecb31f.pdf