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In this paper, we consider a Timoshenko type system coupled with parabolic equation that represents the thermal effect given by the Gurtin-Pipkin law while taking into account that the temperature influences on the shear force. We establish the global existence of solution the behavior of the solution. We also prove the lack of the exponential stability when, we obtain the exponential stability in the case whereand the parameter  p  = 1 and also the polynomial stability in the case whereandsuch that  p  is a parameter related to the thermal memory. One of the novel contribution here is that there is a new number  ξ  that is different from the number of stability that has been proven previously.

Stability of Timoshenko system coupled with thermal law of Gurtin-Pipkin affecting on shear force