Fibonacci wavelet method for solving time-fractional telegraph equations with Dirichlet boundary conditions

Abstract

In this article, a new and efficient operational matrix method based on the amalgamation of Fibonacci wavelets and block pulse functions is proposed for the solutions of time-fractional telegraph equations with Dirichlet boundary conditions. The Fibonacci polynomials and the corresponding wavelets along with their fundamental properties are briefly studied at first. These functions along with their nice characteristics are then utilized to formulate the Fibonacci wavelet operational matrices of fractional integrals. The proposed method reduces the fractional model into a system of algebraic equations, which can be solved using the classical Newton iteration method. Approximate solutions of the time-fractional telegraph equation are compared with the recently appeared Legendre and Sinc-Legendre wavelet collocation methods. The numerical outcomes show that the Fibonacci technique yields precise outcomes and is computationally more effective than the current ones.