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

• Published in: Advances in difference equations 2020-06, Vol.2020 (1), p.1-15, Article 308
• Main Authors: Ghaffar, Abdul, Ali, Ayyaz, Ahmed, Sarfaraz, Akram, Saima, Junjua, Moin-ud-Din, Baleanu, Dumitru, Nisar, Kottakkaran Sooppy
• Format: Article
• Language: English
• Subjects: Analysis; Caputo’s derivative of fractional order; Difference and Functional Equations; Exact solutions; Extended rational exp ( ( ψ ′ ψ ) ( η ) ) $\exp ((\frac{\psi '}{\psi })(\eta ))$ -expansion method; Fractional calculus; Functional Analysis; Hyperbolic functions; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinear evolution equations; Ordinary Differential Equations; Parameters; Partial Differential Equations; Simplified modified Camassa–Holm (SMCH) equation; Solitary wave solutions; Solitary waves
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-020-02751-5

We investigate some solitary wave results of time fractional evolution equations. By employing the extended rational exp ( ( − ψ ′ ψ ) ( η ) ) -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.