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Existence of Nonoscillatory Solutions for Fractional Functional Differential Equations

  • Yong ZhouEmail author
  • Bashir Ahmad
  • Ahmed Alsaedi
Article

Abstract

In this paper, we develop sufficient criteria for the existence of a nonoscillatory solution to the fractional neutral functional differential equation of the form:
$$\begin{aligned} D^{\alpha }_t[x(t)+c x(t-\tau )]'+\sum ^m_{i=1}P_i(t)F_i(x(t-\sigma _i))=0,\quad t\ge t_0, \end{aligned}$$
where \(D_t^{\alpha }\) is Liouville fractional derivatives of order \(\alpha \ge 0\) on the half-axis, \(c\in \mathbb {R}\), \(\tau \), \(\sigma _i\in \mathbb {R}^+\), \(P_i\in C([t_0, \infty ), \mathbb {R})\), \(F_i\in C(\mathbb {R}, \mathbb {R}), ~ i=1,2,\ldots ,m\), \(m \ge 1\) is an integer. Our results are new and improve many known results on the integer-order functional differential equations.

Keywords

Fractional differential equations Liouville derivative Nonoscillatory solutions Existence 

Mathematics Subject Classification

26A33 34K15 35K99 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computational ScienceXiangtan UniversityXiangtanPeople’s Republic of China
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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