Studies on nonlinear fractional Differential equations using Generalized homotopy analysis Method and transform Techniques

Abstract

The computational methods for solving linear and nonlinear fractional differential equations are of essential requirements to analyze various categories of science and engineering problems. Hence, many researchers have developed several mathematical methods to solve the linear and nonlinear fractional differential equations. This dissertation presents new hybrid techniques that are based on the integral transform and Homotopy Analysis Method (HAM) to solve the fractional differential equations and to study the importance of the computational methods through the analysis of solving widely used fractional differential equations. A hybrid computational method Generalized Homotopy Analysis Method (GHAM) based on G-transform and HAM is proposed and applied to solve various categories of linear and nonlinear differential equations. Using GHAM, the closed form series solutions are obtained for the higher-order nonlinear ordinary and partial differential equations and the computational efficiency of the method is studied. Compared to HAM, GHAM completely avoids multiple differentiation and integration in solving higher-order nonlinear differential equations. newline