Fractional Telegraph Equations and its Solution by Natural Transform Decomposition Method

Abstract

In this thesis, Solution of linear and Nonlinear Fractional Telegraph equation by using Natural Transform Decomposition method was successfully implemented in Adomain polynomial sense and the fractional of order β subjected to initial condition. A exact solution technique for solving of linear and Nonlinear Fractional Telegraph equation is presented. Natural Transform Decomposition method is Modified to study this problem, where the derivatives were defined in the fractional sense. Some examples are given to demonstrate the validity and applicability of the method. In examples, we give some example to modified finite difference methods. The obtained exact results reveal that given Natural Transform Decomposed method very good than finite difference methods.The decomposed method provides an semi-analytical solution by using the initial condition only. It produces an efficient explicit solution with high accuracy and minimal calculation. This method provides very efficiently a convergent series solution form with easily computable coefficients. The obtained results show that the Natural Transform decomposition method is very effective and convenient.