A survey of KdV-CDG equations via nonsingular fractional operators
Ihsan Ullah, Aman Ullah, Shabir Ahmad, Hijaz Ahmad, Taher A. Nofal
Abstract
<abstract><p>In this article, the Korteweg-de Vries-Caudrey-Dodd-Gibbon (KdV-CDG) equation is explored via a fractional operator. A nonlocal differential operator with a nonsingular kernel is used to study the KdV-CDG equation. Some theoretical features concerned with the existence and uniqueness of the solution, convergence, and Picard-stability of the solution by using the concepts of fixed point theory are discussed. Analytical solutions of the KdV-CDG equation by using the Laplace transformation (LT) associated with the Adomian decomposition method (ADM) are retrieved. The solutions are presented using 3D and surface graphics.</p></abstract>
Topics & Concepts
Korteweg–de Vries equationInvertible matrixMathematicsUniquenessOperator (biology)Laplace transformConvergence (economics)Sobolev spaceKernel (algebra)Fractional calculusMathematical analysisPure mathematicsApplied mathematicsPhysicsNonlinear systemChemistryGeneTranscription factorEconomic growthQuantum mechanicsEconomicsBiochemistryRepressorFractional Differential Equations SolutionsNonlinear Waves and SolitonsNonlinear Differential Equations Analysis