A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order
Abdul Ghaffar, Ayyaz Ali, Sarfaraz Ahmed, Saima Akram, Moin‐ud‐Din Junjua, Dumitru Bǎleanu, Kottakkaran Sooppy Nisar
Abstract
Abstract We investigate some solitary wave results of time fractional evolution equations. By employing the extended rational $\exp ( (-\frac{{\psi }^{\prime }}{\psi }) ( \eta ) )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>exp</mml:mo><mml:mo>(</mml:mo><mml:mo>(</mml:mo><mml:mo>−</mml:mo><mml:mfrac><mml:msup><mml:mi>ψ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mi>ψ</mml:mi></mml:mfrac><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mi>η</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:math> -expansion method, a few different results including kink, singular-kink, multiple soliton, and periodic wave solutions are formally generated. It is worth mentioning that the solutions obtained are more general with more parameters. The exact solutions are constructed in the form of exponential, trigonometric, rational, and hyperbolic functions. With the choice of proper values of parameters, graphs to some of the obtained solutions are drawn. On comparing some special cases, our solutions are in good agreement with the results published previously and the remaining are new.