Basic existence and a priori bound results for solutions to systems of boundary value problems for fractional differential equations

• Main Author: Christopher C. Tisdell
• Format: Article
• Language: English
• Published: Texas State University 2016-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: Existence of solutions; nonlinear fractional differential equations; boundary value problem; Liapunov function; fixed point theorem
• Online Access: http://ejde.math.txstate.edu/Volumes/2016/84/abstr.html

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 sufficient 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 Schafer. 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. A YouTube video from the author that is designed to complement this research is available at youtube.com/watch?v=cDUrLsQLGvA