INVESTIGATION OF FRACTIONAL ORDER SINE-GORDON EQUATION USING LAPLACE ADOMIAN DECOMPOSITION METHOD

Amir Ali, Zamin Gul (), Wajahat Ali Khan (), Saeed Ahmad () and Salman Zeb ()
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Amir Ali: Department of Mathematics, University of Malakand, Dir(L), KP, Pakistan
Zamin Gul: ��Higher Education Department, Peshawar, KP Pakistan
Wajahat Ali Khan: Department of Mathematics, University of Malakand, Dir(L), KP, Pakistan
Saeed Ahmad: Department of Mathematics, University of Malakand, Dir(L), KP, Pakistan
Salman Zeb: Department of Mathematics, University of Malakand, Dir(L), KP, Pakistan

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-10

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.

Keywords: Fractional Order sG Equation; Adomian Decomposition Method; Laplace Transformations; Iterative Solutions (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501218

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