Arab Journal of Mathematical Sciences (Jul 2021)
Further fresh and general traveling wave solutions to some fractional order nonlinear evolution equations in mathematical physics
Abstract
Purpose – Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional (DξαG/G)-expansion method, to unravel the nonlinear space-time fractional potential Kadomtsev–Petviashvili (PKP) equation, the nonlinear space-time fractional Sharma–Tasso–Olver (STO) equation and the nonlinear space-time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equation. A fractional complex transformation technique is used to convert the considered equations into the fractional order ordinary differential equation. Then the method is employed to make available their solutions. The constructed solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in physics, mathematical physics and engineering. Design/methodology/approach – The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is of the form U(ξ)=∑i=0nai(DξαG/G)i/∑i=0nbi(DξαG/G)i. Findings – Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature. Originality/value – The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is newly established and productive.
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