On conformable fractional calculus

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摘要

Recently, the authors Khalil et al. (2014) introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. In this article we proceed on to develop the definitions there and set the basic concepts in this new simple interesting fractional calculus. The fractional versions of chain rule, exponential functions, Gronwall’s inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed.

论文关键词：Left and right conformable fractional derivatives,Left and right conformable fractional integrals,Fractional Taylor power series expansion,Fractional exponential function,Fractional Gronwall’s inequality,Chain rule

论文评审过程：Received 6 January 2014, Revised 27 July 2014, Available online 29 October 2014.

论文官网地址：https://doi.org/10.1016/j.cam.2014.10.016