INVESTIGATION OF FRACTIONAL ORDER SINE-GORDON EQUATION USING LAPLACE ADOMIAN DECOMPOSITION METHOD
Amir Ali, Zamin Gul, Wajahat Ali Khan, Saeed Ahmad, Salman Zeb
Abstract
We analytically investigate a nonlinear fractional-order sine-Gordon (sG) equation. The derivatives considered herein, are taken in Caputo’s sense. The Laplace transform together with the Adomian decomposition method (LADM) is applied to attain analytical approximation of the aforesaid equation. The sG equation having Caputo derivative is solved in the order of series solutions and the results are confirmed by considering two examples with appropriate initial conditions. The numerical simulations are accomplished to compare with the analytical approximations, where qualitatively better agreements are achieved.
Topics & Concepts
Adomian decomposition methodLaplace transformMathematicsFractional calculusDecomposition method (queueing theory)Laplace's equationMathematical analysisNonlinear systemSineSeries (stratigraphy)Applied mathematicsPartial differential equationPhysicsGeometryBiologyDiscrete mathematicsQuantum mechanicsPaleontologyFractional Differential Equations SolutionsNonlinear Waves and SolitonsIterative Methods for Nonlinear Equations