Atilgan, EmrahSenol, MehmetKurt, AliTasbozan, Orkun2024-09-182024-09-1820190890-54872191-8945https://doi.org/10.1007/s13344-019-0045-1https://hdl.handle.net/20.500.12483/12585The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq-Whitham-Broer-Kaup equation arising as a model of shallow water waves. For this aim, the authors employed auxiliary equation method which is based on a nonlinear ordinary differential equation. By using conformable wave transform and chain rule, a nonlinear fractional partial differential equation is converted to a nonlinear ordinary differential equation. This is a significant impact because neither Caputo definition nor Riemann-Liouville definition satisfies the chain rule. While the exact solutions of the fractional partial derivatives cannot be obtained due to the existing drawbacks of Caputo or Riemann-Liouville definitions, the reliable solutions can be achieved for the equations defined by conformable fractional derivatives.eninfo:eu-repo/semantics/openAccesstime fractional coupled Boussinesq-Whitham-Broer-Kaup equationconformable fractional derivativeauxiliary equation methodArticle33447748310.1007/s13344-019-0045-12-s2.0-85068779403Q2WOS:000475692400009Q4