On Meromorphic Solutions of Some Fermat-Type Functional Equations

In this paper, we study the existence of meromorphic solutions of hyperorder strictly less than 1 to functional equation \(f(z)^{2}+f(z+c)^{3}=e^{P},f(z)^{2}+f(z+c)^{4}=e^{P}\) and the solution of the difference analogue of Fermat-type equation of the form \(f(z)^{3}+[c_{1}f(z+c)+c_{0}f(z)]^{3}=e^{P}\) , where \(P\) is a polynomial. These results generalize the results of Lü and Guo [Mediterr. J. Math. 2022] and Ahamed [J. Contemp. Math. Anal. 2021].