On a Quadratic Nonlinear Fractional Equation

Fractal and Fractional

article

Iván Area¹  Juan J. Nieto² 

[1] CITMAga, Universidade de Vigo, Departamento de Matemática Aplicada II, E.E. Aeronáutica e do Espazo, Campus As Lagoas-Ourense;CITMAga, Universidade de Santiago de Compostela

关键词: logistic ordinary differential equation;    blow-up;    fractional differential equation;    Lambert function;    non-elementary functions;    non-uniqueness34A05;    34A34;    34M50;   

DOI  :  10.3390/fractalfract7060469

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY