Extremal solutions for multi-term nonlinear fractional differential equations with nonlinear boundary conditions

Document Type : Research Paper


Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.


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.


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Volume 11, Issue 1
January 2023
Pages 32-41
  • Receive Date: 07 October 2021
  • Revise Date: 31 December 2021
  • Accept Date: 07 January 2022
  • First Publish Date: 14 January 2022