https://doi.org/10.1140/epjp/i2019-12772-1
Regular Article
Lyapunov type inequalities via fractional proportional derivatives and application on the free zero disc of Kilbas-Saigo generalized Mittag-Leffler functions⋆
1
Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, 11586, Riyadh, Saudi Arabia
2
Department of Mathematics, Çankaya University, 06790, Ankara, Turkey
3
Department of Applied mathematics, Palestine Technical University-Kadoorie, Tulkarm, West Bank, Palestine
* e-mail: fahd@cankaya.edu.tr
Received:
30
January
2019
Accepted:
20
April
2019
Published online:
31
May
2019
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019
