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In this paper we consider a fractional differential system with coupled integral boundary value problems on a half-line, where the nonlinearity terms depend on unknown functions and the lower-order fractional derivative of unknown functions, and the fractional infinite boundary value conditions depend on the coupled infinite integral of unknown functions. By virtue of the monotone iterative technique, we find two explicit monotone iterative sequences which converge to the positive minimal and maximal solutions when the nonlinearities can satisfy certain nonlinear growth conditions.

advances in difference equations

Explicit monotone iterative sequences for positive solutions of a fractional differential system with coupled integral boundary conditions on a half-line