Analytical Solution of One-Dimensional Nonlinear Conformable Fractional Telegraph Equation by Reduced Differential Transform Method

Abstract

In this paper, the reduced differential transform method (RDTM) is successfully implemented to obtain the analytical solution of the space-time conformable fractional telegraph equation subject to the appropriate initial conditions. The fractional-order derivative will be in the conformable (CFD) sense. Some properties which help us to solve the governing problem using the suggested approach are proven. The proposed method yields an approximate solution in the form of an infinite series that converges to a closed-form solution, which is in many cases the exact solution. This method has the advantage of producing an analytical solution by only using the appropriate initial conditions without requiring any discretization, transformation, or restrictive assumptions. Four test modeling problems from mathematical physics, conformable fractional telegraph equations in which we already knew their exact solution using other numerical methods, were taken to show the liability, accuracy, convergence, and efficiency of the proposed method, and the solution behavior of each illustrative example is presented using tabulated numerical values and two- and three-dimensional graphs. The results show that the RDTM gave solutions that coincide with the exact solutions and the numerical solutions that are available in the literature. Also, the obtained results reveal that the introduced method is easily applicable and it saves a lot of computational work in solving conformable fractional telegraph equations, and it may also find wide application in other complicated fractional partial differential equations that originate in the areas of engineering and science.