Numerical optimization algorithm for solving time-fractional telegraph equations

A numerical optimization algorithm utilizing the eighth kind fractional Chebyshev wavelets (EFCWs) in conjunction with the Whale Optimization algorithm (WOA) is developed for solving time-fractional telegraph equations. First, EFCWs are constructed based on the eighth kind Chebyshev polynomials. Subsequently, several properties of EFCWs are analyzed in detail, including the convergence analysis of wavelet expansions and error estimation. Following this, fractional integration formulas of EFCWs are derived under the Riemann-Liouville fractional integral framework. Utilizing these formulas along with the collocation method, a numerical scheme is established by discretizing the time-fractional telegraph equation into a system of equations. Thereafter, WOA is employed to further optimize the proposed numerical algorithm. Finally, specific examples are presented to illustrate the application of this method. The computed results are rigorously analyzed and compared with existing research outcomes. The comparative analysis not only verifies the feasibility and effectiveness of the proposed method but also highlights the potential of WOA in enhancing the performance of the numerical scheme.