Non-Existence of Global Solutions for a Fractional Integro-Differential Problem with a Convolution Kernel

摘要

In this paper, we investigate the nonexistence of nontrivial global solutions for a fractional integro-differential problem in the space of absolutely continuous functions. We provide criteria under which no nontrivial global solutions exist. It is shown that a dissipation of order between zero and one or even a (frictional) dissipation of order one does not help providing global nontrivial solutions. The test function method is used with several derived estimations. Examples with numerical computations are given to illustrate the results.