Abstract
We consider two separate systems of fractional differential equations with exponential non-linearities. We also consider the corresponding systems of non-linear Volterra integral equations. We present results on the non-existence of global solutions for each system. Bounds on the blow-up time for each system are provided along with the asymptotic growth near blow-up. Each system can be regarded as a model for the interaction of two weakly diffusive media subjected to Arrhenius-type reactions. Our results indicate that a thermal blow-up cannot be avoided under such conditions.
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