In this paper, we study the Lyapunov stability of traveling wave solutions for degenerating Fisher type equations with fractional Laplacian. First, we give the asymptotic behavior of the derivative of the traveling wave solutions at negative infinity by using the maximum principle. Second, we construct the subsolution and supersolution of the initial value problem in a moving coordinate frame. Finally, we use the sub-super solution method to prove the Lyapunov stability of traveling wave solutions in the polynomially weighted space.
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