A Robust Numerical Approach for the Fractional Polio Model by the Genocchi Wavelet Collocation Method

This paper proposes an innovative numerical method called the Genocchi wavelet collocation method (GWCM) for the numerical study of fractional Polio model. The newly developed numerical algorithm is based on a functional basis and operational matrices of the Genocchi wavelets generated by the Genocchi polynomials. The desired model is in the form of fractional system of ordinary differential equations (SODE). The developed technique transforms the desired model into a framework of nonlinear algebraic equations with the help of operational matrices and equispaced collocation points. The Newton–Raphson method is used to solve the resulting system and yields an approximate solution of the nonlinear SODEs. The fractional orders in the SODEs are concerned in the Caputo sense. The GWCM findings are further corroborated by the results of the Runge–Kutta and NDSolver techniques to show the effectiveness of the suggested numerical algorithm. The technique’s validity and efficacy are demonstrated using numerical illustration. The acquired numerical results are reasonably consistent with the ND Solver results that have been explained in the tables and figures. The error and convergence analysis of the Genocchi wavelets has been also discussed for the applicability of the present method. The numerical outcomes demonstrate that (GWCM) is incredibly effective and precise for solving the polio model of fractional order. Mathematical software called Mathematica has been used for numerical computations and implementation.