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

Interest on the study of fractional differential equation is on the rise because of its utility in the fields of science and engineering such as neural networks, population dynamics, electrical and mechanical engineering. In recent years, there has been a significant development in fractional order ordinary and partial differential equations, for example Kilbas et al.[6]. In particular, the oscillation theory of fractional differential equations attracted by many authors [1, 2, 5, 7, 8, 10,15–17]. The H-oscillation for vector differential equation was introduced by Domshlak [3] in 1970. Few authors [9,11–13] have discussed H-oscillation of vector partial differential equations. Prakash and Harikrishnan [14] have established criteria for H-oscillation of solutions of impulsive vector hyperbolic differential equations with delays. However, the concept of H-oscillation of vector partial differential equation studied for integer order only. In this paper, we establish sufficient conditions for H-oscillation of a class of time fractional vector diffusion-wave equation with forced and fractional damping terms subject to the Neumann boundary condition by using differential inequality method.