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arXiv · 1411.5616

Positive Green's functions for some fractional-order boundary value problems

Douglas R. Anderson
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Abstract

We use the newly introduced conformable fractional derivative, which is different from the Caputo and Riemann-Liouville fractional derivatives, to reformulate several common boundary value problems, including those with conjugate, right-focal, and Lidstone conditions. With the fractional differential equation and fractional boundary conditions established, we find the corresponding Green's functions and prove their positivity under appropriate assumptions.

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Douglas R. Anderson. 2014-11-20. Positive Green's functions for some fractional-order boundary value problems. https://arxiv.org/abs/1411.5616

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