Combination of Laplace transform and residual power series techniques to solve autonomous <i>n</i> -dimensional fractional nonlinear systems
Marwan Alquran, Maysa Alsukhour, Mohammed Ali, Imad Jaradat
Abstract
Abstract In this work, a new iterative algorithm is presented to solve autonomous n -dimensional fractional nonlinear systems analytically. The suggested scheme is combination of two methods; the Laplace transform and the residual power series. The methodology of this algorithm is presented in details. For the accuracy and effectiveness purposes, two numerical examples are discussed. Finally, the impact of the fractional order acting on these autonomous systems is investigated using graphs and tables.
Topics & Concepts
Laplace transformNonlinear systemResidualSeries (stratigraphy)Two-sided Laplace transformPower seriesMathematicsApplied mathematicsLaplace transform applied to differential equationsInverse Laplace transformElectric power systemAlgorithmMathematical optimizationPower (physics)Control theory (sociology)Computer scienceFractional Fourier transformMathematical analysisArtificial intelligenceFourier transformPhysicsFourier analysisBiologyControl (management)PaleontologyQuantum mechanicsFractional Differential Equations SolutionsAdvanced Control Systems DesignIterative Methods for Nonlinear Equations