On abundant new solutions of two fractional complex models

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.

Keywords

• Fractional Korteweg–de Vries (KdV) equation
• Fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation
• ABR $\mathcal{ABR}$ fractional operator
• Modified Khater (mK) method