Hybrid techniques for approximate analytical solution of space- and time-fractional telegraph equations

This article intends to study the space-fractional and time-fractional telegraph equations using three hybrid methods, viz. Elzaki homotopy perturbation method, Sumudu homotopy perturbation method and Aboodh homotopy perturbation method. The nonlinear terms can be handled by using homotopy perturbation method. The homotopy perturbation method is applied to the reformulated first- and second-order initial value problem which leads the solution in terms of transformed variables, and the series solution is obtained by using the inverse transformation. These three methods give approximate analytical solution in the form of power series and converges to exact solution. This shows the efficiency of the mentioned methods. By these methods, we can get the accuracy of the approximate solutions only after a few terms. For the accuracy of the obtained solutions, the absolute error has been illustrated graphically.