On the oscillation of Hadamard fractional differential equations

• Main Authors: Bahaaeldin Abdalla, Thabet Abdeljawad
• Format: Article
• Language: English
• Published: SpringerOpen 2018-11-01
• Series: Advances in Difference Equations
• Subjects: Fractional Hadamard integrals; Fractional Hadamard derivatives; Fractional differential equations; Oscillation theory
• Online Access: http://link.springer.com/article/10.1186/s13662-018-1870-x

Abstract Hadamard fractional derivatives are nonlocal fractional derivatives with singular logarithmic kernel with memory, and hence they are suitable to describe complex systems. In this paper, sufficient conditions are established for the oscillation of solutions fractional differential equations in the frame of left Hadamard fractional derivatives of order α∈C,Re(α)≥0 $\alpha\in\mathbb {C}, \operatorname{Re}(\alpha)\geq0$. The results are also obtained for fractional Hadamard derivatives in the Caputo setting. Examples are provided to illustrate the applicability of the main results.