Estimates of higher order fractional derivatives at extreme points

Volume 10, Issue 10, pp 5174--5181

Publication Date: 2017-10-12

http://dx.doi.org/10.22436/jnsa.010.10.05

Authors

Mohammed Al-Refai - Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, UAE
Dumitru Baleanu - Department of Mathematics and Computer Science, Cankaya University, 06530 Ankara, Turkey

Abstract

We extend the results concerning the fractional derivatives of a function at its extreme points to fractional derivatives of arbitrary order. We also give an estimate of the error and present two examples to illustrate the validity of the results. The presented results are valid for both Caputo and Riemann-Liouville fractional derivatives.

Keywords

Extreme points, higher order fractional derivatives, Caputo derivative, Riemann-Liouville derivative

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