Monotonicity and convexity results for a function through its Caputo fractional derivative

Mohammed Al-Refai

doi:10.1515/fca-2017-0042

Monotonicity and convexity results for a function through its Caputo fractional derivative

Mohammed Al-Refai

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper we discuss certain geometric properties of a function through its Caputo fractional derivative. We show that convexity and monotonicity results can be obtained provided that the fractional derivative of the function is of one sign for some value of α. Analogous result for the global extrema of a function is obtained. However, to release the condition on the Diethelm paper [3] that the fractional derivative of the function is of one sign for all values of α in certain domain, higher order fractional inequalities are required. The applicability of the new results is discussed.

Original language	English
Pages (from-to)	818-824
Number of pages	7
Journal	Fractional Calculus and Applied Analysis
Volume	20
Issue number	3
DOIs	https://doi.org/10.1515/fca-2017-0042
Publication status	Published - Jun 27 2017

Keywords

Caputo fractional derivative
convexity
fractional calculus
monotonic functions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1515/fca-2017-0042

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AB - In this paper we discuss certain geometric properties of a function through its Caputo fractional derivative. We show that convexity and monotonicity results can be obtained provided that the fractional derivative of the function is of one sign for some value of α. Analogous result for the global extrema of a function is obtained. However, to release the condition on the Diethelm paper [3] that the fractional derivative of the function is of one sign for all values of α in certain domain, higher order fractional inequalities are required. The applicability of the new results is discussed.

KW - Caputo fractional derivative

KW - convexity

KW - fractional calculus

KW - monotonic functions

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Monotonicity and convexity results for a function through its Caputo fractional derivative

Abstract

Keywords

ASJC Scopus subject areas

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