Time-Fractional Hyperbolic Telegraph Equation: A Semi-Analytic Approach Using Modified Adomian Decomposition Elzaki Transform Method

Abstract

In this research paper, an approximate analytical solution approach known as the Modified Adomian Decomposition Method with the coupling of Elzaki Transform (MADETM) is deployed for addressing one-dimensional, two- dimensional, and three-dimensional time-fractional hyperbolic telegraph equations. The Caputo derivative operator yields the approximate analytical solution. The impact ness and its accuracy of the adopted method are demonstrated through comparison of the approximate results with the exact solutions, both presented graphically by plotting its surface graph, line graph through analyzing its error. The MADETM proves to be a reliable and efficient tool for deriving approximate and exact solutions for a large class of partial differential equations (PDEs), fractional PDEs, and ordinary differential equations (ODEs). The considered method yields a solution in series form with low computational complexity and swiftly converges towards precise solutions. The outcomes showcase an effective and uncomplicated approach for examining issues across diverse scientific and technological domains.