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Browsing by Author "Mallak, Saed F."

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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
    (Springer Heidelberg, 2019) Abdeljawad, Thabet; Jarad, Fahd; Alzabut, Jehad; Alzabut, Jehad; 234808
    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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    Article
    Lyapunov type inequality in the frame of Generalized caputo derivatives
    (2021) Jarad, Fahd; Abdeljawad, Thabet; Abdeljawad, Thabet; Mallak, Saed F.; Alrabaiah, Hussam; 234808
    In this paper, we establish the Lyapunov-type inequality for bound- A ry value problems involving generalized Caputo fractional derivatives that unite the Caputo and Caputo-Hadamrad fractional derivatives. An applica-tion about the zeros of generalized types of Mittag-Leffler functions is given. © 2021 American Institute of Mathematical Sciences. All rights reserved.