An Efficient Technique to Solve Time-Fractional Kawahara and Modified Kawahara Equations

In this article, we analysed the approximate solutions of time-fractional Kawahara equation and modified equation, which describe propagation signals in transmission lines formation nonlinear water waves long wavelength region. An efficient technique, namely natural transform decomposition method, is used present study. Fractional derivatives are considered Caputo, Caputo–Fabrizio, Atangana–Baleanu operative Caputo manner. We have presented numerical results graphically to demonstrate applicability efficiency with fractional order depict regions. The symmetry pattern a fundamental feature symmetrical aspect solution can be seen from graphical representations. obtained outcomes proposed method compared those other well-known techniques, such as homotopy analysis residual power series method. Numerical converge exact equations, demonstrating significance our