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New Monotonicity Conditions in Discrete Fractional Calculus with Applications to Extremality Conditions by Rajendra Dahal; Stanley Drvol; Christopher S. Goodrich is a Mathematics article available to read on EtoBox.

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## Abstract We present some initial results for detecting extrema of a function f : N a → R {f:\mathbb{N}\_{a}\rightarrow\mathbb{R}} when the only a priori information is some limited pointwise data about __f__ as well as information about an appropriate fractional difference of __f__. In particular, such results provide some analogues of the well-known tests for detecting local extrema using the sign of Δ ⁢ f ⁢ ( t ) {\Delta f(t)} . Certain of these results are consequences of some new monotonicity conditions, which relate conditions on the sign of Δ a ν ⁢ f ⁢ ( t ) {\Delta\_{a}^{\nu}f(t)} , for 0 < ν < 1 {0<\nu<1} , to the monotonicity of __f__. Finally, we provide some numerical examples to illustrate the results.

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Author

Rajendra Dahal; Stanley Drvol; Christopher S. Goodrich

Publisher

Walter de Gruyter GmbH

Published

2017

Language

EN

Field

Mathematics (Physical Sciences)