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α-fractionally convex functions

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Abstract

In this article, we introduce the concept of α-fractionally convex functions. We primarily focus on characterizing some of the qualitative properties of convex functions with the assistance of fractional order operators. Also, we discuss the connection of optimality, monotonicity, and convexity of a function in the sense of fractional calculus. Several examples are provided to support the proposed formulation, and one can establish the fractional convexity of a non-convex function.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal, 721302, India

    Neelam Singha & Chandal Nahak

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  1. Neelam Singha
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  2. Chandal Nahak
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Correspondence to Neelam Singha.

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Singha, N., Nahak, C. α-fractionally convex functions. Fract Calc Appl Anal 23, 534–552 (2020). https://doi.org/10.1515/fca-2020-0026

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