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2013•The Scientific World JOURNALOpen access

Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions

Xian‐Feng Zhou, Song Liu, Zhixin Zhang, Wei Jiang

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Abstract

The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. Then we discuss monotonicity, concavity, and convexity of fractional derivative of some functions and derive corresponding criteria. Several examples are provided to illustrate the applications of our results.

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What this paper is about

The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. Then we discuss monotonicity, concavity, and convexity of fractional derivative of some functions and derive corresponding criteria. Several examples are provided to illustrate the applications of our results.

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Available abstract

The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. Then we discuss monotonicity, concavity, and convexity of fractional derivative of some functions and derive corresponding criteria. Several examples are provided to illustrate the applications of our results.

Key concepts: Monotonic function, Convexity, Fractional calculus, Applied mathematics, Derivative (finance), Mathematics, Class (philosophy), Nonlinear system

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