NUMERICAL ANALYSIS OF FRACTIONAL-ORDER EMDEN–FOWLER EQUATIONS USING MODIFIED VARIATIONAL ITERATION METHOD
RI ZHANG, Nehad Ali Shah, Essam Rashdy El-Zahar, Ali Akgül, Jae Dong Chung
Abstract
This work aims at a new semi-analytical method called the variational iteration transform method for investigating fractional-order Emden–Fowler equations. The Shehu transformation and the iterative method are applied to achieve the solution of the given problems. The proposed method has the edge over other techniques as it does not required extra calculations. Some numerical problems are used to test the validity of the suggested method. The solution obtained has demonstrated that the proposed technique has a higher level of accuracy. The proposed method is capable of tackling various nonlinear fractional-order problems due to its simple implementation.
Topics & Concepts
MathematicsTransformation (genetics)Simple (philosophy)Applied mathematicsNonlinear systemIterative methodNumerical analysisWork (physics)Enhanced Data Rates for GSM EvolutionOrder (exchange)Fractional calculusMathematical analysisMathematical optimizationComputer sciencePhilosophyMechanical engineeringEpistemologyEngineeringQuantum mechanicsFinanceChemistryGeneTelecommunicationsPhysicsEconomicsBiochemistryFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNonlinear Waves and Solitons