Electron. J. Diff. Equ., Vol. 2016 (2016), No. 84, pp. 1-9.

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

Christopher C. Tisdell

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

Submitted February 18, 2016. Published March 23, 2016.
Math Subject Classifications: 34A08.
Key Words: Existence of solutions; nonlinear fractional differential equations; boundary value problem; Liapunov function; fixed point theorem.

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Christopher C. Tisdell
School of Mathematics and Statistics
The University of New South Wales
UNSW Sydney NSW 2052, Australia
email: cct@unsw.edu.au

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