Automatic continuity of almost conjugate Jordan homomorphism on Fr\acute{\text{e}}chet Q-algebras

In this paper, the notation of almost conjugate Jordan homomorphism between Fr\acute{\mathbf{\text{e}}}chet algebras is introduced. It is proven that, under special hypotheses, every  almost conjugate Jordan homomorphism on  Fr\acute{\mathbf{\text{e}}}chet algebras is an (weakly) almost homomorphism. Also, the automatic continuity of them is generalized.