Estimates of higher order fractional derivatives at extreme points
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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.
- Institute of Space Sciences, Magurele-Bucharest, Romania.
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.
Share and Cite
ISRP Style
Mohammed Al-Refai, Dumitru Baleanu, Estimates of higher order fractional derivatives at extreme points, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 5174--5181
AMA Style
Al-Refai Mohammed, Baleanu Dumitru, Estimates of higher order fractional derivatives at extreme points. J. Nonlinear Sci. Appl. (2017); 10(10):5174--5181
Chicago/Turabian Style
Al-Refai, Mohammed, Baleanu, Dumitru. "Estimates of higher order fractional derivatives at extreme points." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 5174--5181
Keywords
- Extreme points
- higher order fractional derivatives
- Caputo derivative
- Riemann-Liouville derivative
MSC
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