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Lyapunov type inequalities via fractional proportional derivatives and application on the free zero disc of Kilbas-Saigo generalized Mittag-Leffler functions⋆

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Abstract.

In this article, we prove Lyapunov type inequalities for a nonlocal fractional derivative, called fractional proportional derivative, generated by modified conformable or proportional derivatives in both Riemann-Liuoville and Caputo senses. Further, in the Riemann-Liuoville case we prove a Lyapunov inequality for a fractional proportional weighted boundary value problem and apply it on a weighted Sturm-Liouville problem to estimate an upper bound for the free zero disk of the Kilbas-Saigo Mittag-Leffler functions of three parameters. The proven results generalize and modify previously obtained results in the literature.

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Authors and Affiliations

  1. Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, 11586, Riyadh, Saudi Arabia

    Thabet Abdeljawad & Jehad Alzabut

  2. Department of Mathematics, Çankaya University, 06790, Ankara, Turkey

    Fahd Jarad

  3. Department of Applied mathematics, Palestine Technical University-Kadoorie, Tulkarm, West Bank, Palestine

    Saed F. Mallak

Authors
  1. Thabet Abdeljawad
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  2. Fahd Jarad
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  3. Saed F. Mallak
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  4. Jehad Alzabut
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Correspondence to Fahd Jarad.

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Abdeljawad, T., Jarad, F., Mallak, S.F. et al. Lyapunov type inequalities via fractional proportional derivatives and application on the free zero disc of Kilbas-Saigo generalized Mittag-Leffler functions⋆. Eur. Phys. J. Plus 134, 247 (2019). https://doi.org/10.1140/epjp/i2019-12772-1

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