Adequate closed form wave solutions to the space–time fractional nonlinear equations in physical sciences

Abstract

Signal processing, water wave mechanics, waves in electro-hydro-dynamic systems, traffic flows, optical fibers, sound waves, etc. can be superbly illustrated through fractional nonlinear evolution equations, such as the time-fraction Zakharov–Kuznetsov (ZK) equation and the space–time fractional modified Korteweg–de Vries (mKdV) equation. The​ fractional derivative is considered in the sense of beta-derivative. In this study, the compatible and broad-ranging closed form soliton solutions to the stated models by making use of the exp(−τη)-expansion method with the assistance of the traveling wave transformation have been investigated. The physical significance of the obtained solutions for the definite values of the associated parameters is analyzed graphically to contrivance the tangible phenomena. It is established that the exp(−τη)-expansion method is convenient, efficient and provide further advanced solutions that can support to construct scores of wave solutions to diverse models.

Keywords

• Traveling wave transformation
• exp(−τ(η))-expansion method
• NLPDE
• Fractional ZK equation
• Fractional mKdV equation