Monotone iterative technique for a sequential delta-Caputo fractional differential equations withnonlinear boundary conditions

Abstract. In this article, we discuss the existence of extremal solutions for a class of nonlinear sequential δ–Caputo fractional differential equations involving nonlinear boundary conditions. Our results are founded on advanced functional analysis methods. To be more specific, we use the monotone iterative approach in conjunction with the upper and lower solution method to create adequate requirements for the existence of extremal solutions. As an application, we give an example to illustrate our results. Mathematics Subject Classification (2010): 34A08, 26A33. Keywords: Sequential δ–Caputo derivative, nonlinear boundary conditions, monotone iterative technique, upper and lower solutions.