| Abstract: |
| We investigated the necessary condition for the following nonlinear system of fractional differential equations to have a blowing-up solution in finite time
$$u'(t) + D_{0|t}^{\alpha(t)} (u(t) - u_0) = |v(t)|^q, t > 0, q > 1 ,$$
and
$$v'(t) + D_{0|t}^{\beta(t)} (v(t) - v_0) = |u(t)|^p, t > 0, p > 1$$
where $u(0) = u_0 > 0, v(0) = v_0 > 0, \alpha, \beta \in C^1[0,+\infty)$ such that $0 < \alpha_m \leq \alpha(t) \leq \alpha_M < 1$ and $0 < \beta_m \leq \beta(t) \leq \beta_M < 1$ and $D_{0|t}^{\rho(t)}$ is Riemann-Liouville derivative of order $\rho(t)$. Our method was to use a suitable test function in the weak functions. |
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