Opuscula Math. 40, no. 2 (2020), 291-305
https://doi.org/10.7494/OpMath.2020.40.2.291

Opuscula Mathematica

# Oscillation of time fractional vector diffusion-wave equation with fractional damping

R. Ramesh
S. Harikrishnan
J. J. Nieto
P. Prakash

Abstract. In this paper, sufficient conditions for $$H$$-oscillation of solutions of a time fractional vector diffusion-wave equation with forced and fractional damping terms subject to the Neumann boundary condition are established by employing certain fractional differential inequality, where $$H$$ is a unit vector in $$\mathbb{R}^n$$. The examples are given to illustrate the main results.

Keywords: fractional diffusion-wave equation, $$H$$-oscillation, vector differential equation.

Mathematics Subject Classification: 35B05, 35R11, 34K37.

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• J. J. Nieto
• https://orcid.org/0000-0001-8202-6578
• Universidad de Santiago de Compostela, Facultad de Matemáticas, Departamento de Análisis Matematico, Santiago de Compostela, Spain
• King Abdulaziz University, Department of Mathematics, Jeddah 21589, Saudi Arabia
• Communicated by Dušan D. Repovš.
• Revised: 2019-10-23.
• Accepted: 2019-11-03.
• Published online: 2020-03-09.