A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order

Abstract

Abstract We investigate some solitary wave results of time fractional evolution equations. By employing the extended rational exp ( ( − ψ ′ ψ ) ( η ) ) $\exp ( (-\frac{{\psi }^{\prime }}{\psi }) ( \eta ) )$ -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.

Keywords

• Simplified modified Camassa–Holm (SMCH) equation
• Fractional calculus
• Caputo’s derivative of fractional order
• Solitary wave solutions
• Extended rational exp ( ( ψ ′ ψ ) ( η ) ) $\exp ((\frac{\psi '}{\psi })(\eta ))$ -expansion method