BASIC EXISTENCE AND A PRIORI BOUND RESULTS FOR SOLUTIONS TO SYSTEMS OF BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS.

This article examines the qualitative properties of solutions to systems of boundary value problems involving fractional differential equations. Our primary interest is in forming new results that involve suficient conditions for the existence of solutions. To do this, we formulate some new ideas concerning a priori bounds on solutions, which are then applied to produce the novel existence results. The main techniques of the paper involve the introduction of novel fractional differential inequalities and the application of the fixed-point theorem of Schäfer. We conclude the work with several new results that link the number of solutions to our problem with a fractional initial value problem, akin to an abstract shooting method. [ABSTRACT FROM AUTHOR]