Application of Elzaki Transform Decomposition Method in Solving Time-Fractional Sawada Kotera Ito Equation

The research paper primarily focuses on the theoretical framework and mathematical methodology for solving the Sawada Kotera Ito with time fraction (SKI) equation using the Elzaki transform decomposition technique, including the Caputo-Fabrizio derivative and the Atangana-Baleanu derivative, which are crucial for comprehending the fractional SKI (1). Various numerical examples are given to illustrate the application of the Elzaki transform in solving the fractional SKI equation. We utilize efficient basis functions, namely fractional Lagrange functions, for the interpolation of temporal variables. By integrating the primary equation with the initial-boundary conditions andemploying the relevant operational matrices for spatial and fractional temporal variables, the proposed model is converted into a system of nonlinear algebraic equations, which can be resolved using effective iterative solvers. Furthermore, we conduct a comprehensive analysis of the method’s convergence. Furthermore, we evaluate multiple test issues to assess the proposed scheme, which demonstrates its superior accuracy and less computational expense compared to contemporary numerical methods in the literature.