Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations
Pshtiwan Othman Mohammed, J. A. Tenreiro Machado, Juan L. G. Guirao, Ravi P. Agarwal
Abstract
Nonlinear fractional differential equations reflect the true nature of physical and biological models with non-locality and memory effects. This paper considers nonlinear fractional differential equations with unknown analytical solutions. The Adomian decomposition and the fractional power series methods are adopted to approximate the solutions. The two approaches are illustrated and compared by means of four numerical examples.
Topics & Concepts
Adomian decomposition methodNonlinear systemMathematicsSeries (stratigraphy)Decomposition method (queueing theory)Power seriesFractional calculusMathematical analysisApplied mathematicsClass (philosophy)Differential equationPhysicsComputer scienceArtificial intelligencePaleontologyQuantum mechanicsBiologyDiscrete mathematicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisIterative Methods for Nonlinear Equations