On a Quadratic Nonlinear Fractional Equation

Abstract

In this paper, we study a quadratic nonlinear equation from the fractional point of view. An explicit solution is given in terms of the Lambert special function. A new phenomenon appears involving the collapsing of the solution and the blow-up of the derivative. The explicit representation of the solution reveals the non-elementary nature of the solution.

Keywords

• logistic ordinary differential equation
• blow-up
• fractional differential equation
• Lambert function
• non-elementary functions
• non-uniqueness