Estimates of higher order fractional derivatives at extreme points

Al-Refai, Mohammed ¹ ; Baleanu, Dumitru²

¹ Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, UAE
² Department of Mathematics and Computer Science, Cankaya University, 06530 Ankara, Turkey;Institute of Space Sciences, Magurele-Bucharest, Romania

Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 10, p. 5174-5181.

Résumé

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.

Détail

DOI : 10.22436/jnsa.010.10.05

Classification : 26A33
Keywords: Extreme points, higher order fractional derivatives, Caputo derivative, Riemann-Liouville derivative

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