ISSN: 1304-7191 | E-ISSN: 1304-7205
Lie symmetry analysis of Caputo time-fractional K(m,n) model equations with variable coefficients
1Department of Mathematics, Istanbul Ticaret University, Istanbul, 34840, Türkiye
Sigma J Eng Nat Sci 2024; 42(3): 885-899 DOI: 10.14744/sigma.2024.00078
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In 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 Capu-to 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.