Employing the Sadik Residual Power Series Method to Analyze a System of Nonlinear Caputo Time-Fractional Partial Differential Equations

The present study proposes an approximate analytical solution to a nonlinear system of time-fractional partial differential equations. The Sadik residual power series method, which integrates the two-part Sadik integral transform with the residual power series technique, is employed to solve the fractional differential equation in the Caputo sense. Nonlinear problems with known and unknown solutions are examined to demonstrate the capacity of the technique. Numerical simulations and 3D visualizations are conducted for various values of the fractional order to further understand the solution’s behavior. Additionally, the results are validated against exact solutions or existing methodologies to ensure their reliability and accuracy. A key advantage of the proposed method is its ability to generate results without the need for Adomian polynomials, perturbation techniques, discretization, or linearization, enabling a more efficient.