Abstract
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.
Highlights
1 Introduction Fractional-order differential equations is a natural generalization of the case of integer order, which has become the focus of attention involving various kinds of boundary conditions because of the wide application in mathematical models and applied sciences
We note that there are some results about monotone iterative solution of a single fractional order equation on a half-line, see [25,26,27,28,29]
Inspired by the works above, in this paper we utilize the monotone iterative technique to study the existence of positive extremal solutions of a fractional differential system on a half-line
Summary
Fractional-order differential equations is a natural generalization of the case of integer order, which has become the focus of attention involving various kinds of boundary conditions because of the wide application in mathematical models and applied sciences. We note that there are some results about monotone iterative solution of a single fractional order equation on a half-line, see [25,26,27,28,29]. A large number of results about fractional differential equations with integral boundary condition have been obtained, see [9, 10, 30,31,32,33,34,35,36,37,38,39,40,41,42,43] and the references cited therein.
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