Genocchi Wavelet Method for the Solution of Time-Fractional Telegraph Equations with Dirichlet Boundary Conditions

Abstract

The present paper suggests a novel, efficient operational matrix technique on the basis of block-pulse functions and Genocchi wavelets to solve time-fractional telegraph equations considering Dirichlet boundary conditions. First, a brief overview of the Genocchi polynomials, corresponding wavelets, and fundamental characteristics is presented. Then, the same functions and their suitable characteristics are employed to formulate the Genocchi wavelet-like operational matrices of fractional integration. Using the suggested technique, the fractional model is reduced into a system of algebraic equations, which is solvable by employing the classical Newton’s iteration technique. A comparison is made between the estimated solutions of the time-fractional telegraph equation and the present approaches, such as the Legendre wavelet and the Fibonacci wavelet method. According to the numerical results, accurate results are obtained using the Genocchi method, and therefore, it is computationally more effective compared to the present approaches.