Adequate wide-ranging closed-form wave solutions to a nonlinear biological model

Abstract

The auxiliary equation method and the extended tanh function method are put in use to establish wide-ranging, further general and standard closed-form traveling wave solutions to the time fractional nonlinear biological model. The fractional derivative is considered in the sense of beta-derivative. The ascertained solutions are in the form of exponential, rational, hyperbolic and trigonometric functions with significant physical meaning. The achieved solutions demonstrate that the methods are effective, compatible and efficient mathematical tools. We analyze the attained solutions through sketching graphs for the defined values of the associated parameters to perceive the internal structure by making use the Mathematica software. The developed traveling wave solutions might be helpful to illustrate the internal infrastructure of tangible phenomena associated with the consider model.