Optimal solution of the nonlinear time-fractional diffusion-wave equation using generalized Laguerre polynomials

Determining the numerical solutions of a nonlinear fractional differential equation has been of interest for a long time. This study presents an optimization method with Lagrange coefficients based on operational matrices of derivatives to approximate the solution by selecting appropriate basis functions as a linear combination of generalized Laguerre polynomials (GLPs). Achieving an exact solution using fewer basis functions is one of the outstanding features of this method. This feature and high accuracy make the use of this method inevitable. Finally, the application of the mentioned method is investigated in determining the approximate solution of the nonlinear fractional time diffusion-wave equation for different values of \alpha.

کلیدواژه ها:

fractional calculus ، Fractional diffusion-wave equation ، Generalized Laguerre polynomials ، Operational matrix ، Caputo fractional derivative ، Control parameters ، Free coefficients