Abstract
In this research we are interested to Cauchy problem for system of semi-linear fractional evolution equations. Some authors were concerned with studying of global existence of solutions for the hyperbolic nonlinear equations with a damping term. Our goal is to extend some results obtained by the authors, by studying the system of semi-linear hyperbolic equations with fractional damping term and fractional Laplacian .Thanks to the test functions method, we prove the nonexistence of nontrivial global weak solutions to the problem.
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