On abundant new solutions of two fractional complex models
Mostafa M. A. Khater, Dumitru Bǎleanu
Abstract
Abstract We use an analytical scheme to construct distinct novel solutions of two well-known fractional complex models (the fractional Korteweg–de Vries equation (KdV) equation and the fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation). A new fractional definition is used to covert the fractional formula of these equations into integer-order ordinary differential equations. We obtain solitons, rational functions, the trigonometric functions, the hyperbolic functions, and many other explicit wave solutions. We illustrate physical explanations of these solutions by different types of sketches.
Topics & Concepts
MathematicsKorteweg–de Vries equationPartial differential equationOrdinary differential equationFractional calculusRational functionOrder (exchange)TrigonometryDifferential equationApplied mathematicsMathematical analysisPure mathematicsNonlinear systemPhysicsQuantum mechanicsFinanceEconomicsNonlinear Waves and SolitonsFractional Differential Equations SolutionsNonlinear Photonic Systems