Nonexistence of global solutions of systems of time fractional differential equations posed on the Heisenberg group

摘要

We first consider a nonlinear time fractional wave equation with a fractional damping posed on the Heisenberg group with Caputo fractional derivatives that interpolate the heat equation and the wave equation with the linear damping. It extends the Caputo–Wisner, the modified Szabo and the fractional Zener models. The non‐linearity accounts for a nonlinear medium. We present the Fujita exponent for blow‐up which sheds light on the admissible nonlinearity in practice. Then, we establish sufficient conditions ensuring non‐existence of local solutions. using the nonlinear capacity method. Furthermore, we extend the analysisto the case of the 2×2 system to show the flexibility of the method used.