İSkenderoğlu, GülistanKaya, Doğan2024-10-122024-10-1220241304-7191https://doi.org/10.14744/sigma.2024.00078https://hdl.handle.net/11467/8821In this study, we consider model equations K(m,n) with fractional Caputo time derivatives. By applying the Lie group symmetry method, we determine all symmetries for these equations and present the reduced symmetric equations for the equation K(m,n) with fractional Caputo time derivatives. Furthermore, we obtain the exact solution for K(1,1) with the fractional Caputo time derivative and provide graphs depicting the behavior at different orders of the fractional time derivative. Additionally, by considering the symmetries of the equation, we establish the conservation laws for K(m,m) with the fractional Caputo time derivative. Copyright 2021, Yıldız Technical University.eninfo:eu-repo/semantics/openAccessConservation LawsFractional CalculusLie GroupsNonlinear Differential EquationsArticle423885899N/A2-s2.0-8520063123510.14744/sigma.2024.00078