A class of traveling wave solutions for space–time fractional biological population model in mathematical physics

Abstract

The \((\frac{G'}{G})\)-expansion method is utilized for a reliable treatment of space–time fractional biological population model. The method has been applied in the sense of the Jumarie’s modified Riemann–Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the \((\frac{G'}{G})\)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.