A convexity result for fractional differences

作者：Goodrich Christopher S^*

来源：Applied Mathematics Letters, 2014, 35: 58-62.

DOI：10.1016/j.aml.2014.04.013

• Discrete fractional calculus
• Convexity
• Nonexistence of solution
• Boundary value problem
• (N-1, 1) problem

In this brief note we demonstrate that under certain conditions the positivity of the fractional difference Delta(mu)(0)y(t), for a given function y : N-0 -%26gt; IR and a number mu is an element of(2, 3), implies the convexity of y. This is given as a special case of a more general result. Finally, as a concrete application of this result we demonstrate that a particular class of fractional boundary value problems has no nontrivial positive solutions.

• 出版日期2014-9