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Sturm–Picone comparison theorem of a kind of conformable fractional differential equations on time scales

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Abstract

In this paper, we consider the Sturm–Picone comparison theorem of conformable fractional differential equations on arbitrary time scales. Since the Picone identity plays an important role in discussing the Sturm comparison theorem. Firstly, we establish the Picone identity of conformable fractional differential equations on arbitrary time scales. By using this identity, we obtain our main result—the Sturm–Picone comparison theorem of conformable fractional differential equations on time scales. This result not only extends and improves the corresponding continuous and discrete time statement, but also contains the usual time scale case when the order of differentiation is one.

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Acknowledgments

This research was supported by the NNSF of China (Grant 11571202) and the NSF of University of Jinan (XKY1511).

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  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, China

    Chao Zhang & Shurong Sun

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  1. Chao Zhang
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  2. Shurong Sun
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Correspondence to Chao Zhang.

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Zhang, C., Sun, S. Sturm–Picone comparison theorem of a kind of conformable fractional differential equations on time scales. J. Appl. Math. Comput. 55, 191–203 (2017). https://doi.org/10.1007/s12190-016-1032-9

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  • DOI: https://doi.org/10.1007/s12190-016-1032-9

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