Fractional Series Solution Construction for Nonlinear Fractional Reaction-Diffusion Brusselator Model Utilizing Laplace Residual Power Series

Residual Power Series Method for Solving Time-fractional Model of Vibration Equation of Large Membranes

The primary aim of this manuscript is to present the approximate analytical solutions of the time fractional order α (1<α≤2) Vibration Equation (VE) of large membranes with the use of an iterative technique namely Residual Power Series Method (RPSM). The fractional derivative is defined in the Caputo sense. Example problems have been solved to demonstrate the efficacy of the present method and ...

Series Solution of Nonlinear Dynamic System Containing Fractional Derivative

Series solution of nonlinear dynamic system containing fractional derivative is obtained by the homotopy analysis method (HAM). The solution via HAM has auxiliary parameter h̄ which can control the convergent of the series to obey the exact or numerical solution. The model of viscoelastic behavior of a one-degree-of-freedom oscillator consisting of a discrete mass and a viscoelastic spring is co...

Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation

The approximate analytical solution of fractional order, nonlinear, reaction differential equations, namely the nonlinear diffusion equations, with a given initial condition, is obtained by using the homotopy analysis method. As a demonstration of a good mathematical model, the present article gives graphical presentations of the effect of the reaction terms on the solution profile for various ...

Approximate Series Solution of Nonlinear, Fractional Klein- Gordon Equations Using Fractional Reduced Differential Transform Method

Corresponding Author: Mohammed Al-Smadi Department of Applied Science, Ajloun College, AlBalqa Applied University, Ajloun 26816, Jordan Email: [email protected] Abstract: This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Red...

Neumann-Series Solution of Fractional Differential Equation