Numerical Solutions of Time Fractional Zakharov-Kuznetsov Equation via Natural Transform Decomposition Method with Nonsingular Kernel Derivatives
Zhou Meixiu, A.S.V. Ravi Kanth, K. Aruna, K. Raghavendar, Hadi Rezazadeh, Ayman A. Aly
Abstract
In this paper, we have studied the time-fractional Zakharov-Kuznetsov equation (TFZKE) via natural transform decomposition method (NTDM) with nonsingular kernel derivatives. The fractional derivative considered in Caputo-Fabrizio (CF) and Atangana-Baleanu derivative in Caputo sense (ABC). We employed natural transform (NT) on TFZKE followed by inverse natural transform, to obtain the solution of the equation. To validate the method, we have considered a few examples and compared with the actual results. Numerical results are in accordance with the existing results.
Topics & Concepts
Invertible matrixMathematicsKernel (algebra)Fractional calculusInverseDecomposition method (queueing theory)DecompositionDerivative (finance)Applied mathematicsMathematical analysisPure mathematicsDiscrete mathematicsGeometryEcologyFinancial economicsEconomicsBiologyFractional Differential Equations SolutionsNonlinear Waves and SolitonsNumerical methods for differential equations