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Oscillation for Fractional Partial Differential Equations

  • Yong Zhou
  • Bashir Ahmad
  • Fulai Chen
  • Ahmed Alsaedi
Article

Abstract

In this paper, we develop the sufficient criteria for the oscillation of all solutions to the following fractional functional partial differential equation involving Riemann–Liouville fractional derivative equipped with initial and Neumann, Dirichlet and Robin boundary conditions:
$$\begin{aligned} \displaystyle \frac{\partial ^{\alpha } u(x, t)}{\partial t^{\alpha }}=C(t)\triangle u+\displaystyle \sum \limits _{i=1}^{n}P_i(x)u(x, t-\sigma _i)+R(x, t), \end{aligned}$$
(1.1)
where \(0<\alpha <1\), \((x, t)\in \Omega \times (0, \infty )\), \(\Omega \) is a bounded domain in Euclidean \(n-\)dimensional space \(\mathbb {R}^n\) with a piecewise smooth boundary \(\partial \Omega \); \(C\in C((0,\infty ),(-\infty ,0]),\)\(\triangle \) is the Laplacian in \(\mathbb {R}^\texttt {n}, P_i\in C(\Omega ,[0,\infty )), R(x,t)\in C(G, (-\infty ,\infty )), \sigma _i\in [0,\infty ), i=1,2,\ldots ,n\).

Keywords

Oscillation Fractional partial differential equations Delay Laplace transform Riemann–Liouville derivative 

Mathematics Subject Classification

26A33 34K15 35K99 44A10 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  • Yong Zhou
    • 1
    • 2
  • Bashir Ahmad
    • 2
  • Fulai Chen
    • 3
  • Ahmed Alsaedi
    • 2
  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
  3. 3.Department of MathematicsXiangnan UniversityChenzhouPeople’s Republic of China

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