On a system of finitely many nonlinear Riemann–Liouville fractional differential equations with fractional anti-periodic boundary conditions

Abstract In this paper, we introduce a coupled system of n nonlinear Riemann–Liouville fractional differential equations each of order in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mn>2</m:mn> <m:mo>,</m:mo> <m:mn>3</m:mn> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(2,3)} and equipped with fractional anti-periodic boundary conditions. We explore the existence and uniqueness criteria for solutions of the given problem by means of Leray–Schauder’s alternative and Banach’s contraction mapping principle in a weighted space. The Ulam–Hyers stability is also studied for the problem at hand. Examples are presented to illustrate the main results.