Fractional-order Riccati differential equation: Analytical approximation and numerical results

Advances in Difference Equations

Asmat Ara¹  Najeeb Alam Khan²  Nadeem Alam Khan² 

[1] Department of Mathematical Sciences, Federal Urdu University Arts, Science and Technology, Karachi, Pakistan;Department of Mathematical Sciences, University of Karachi, Karachi, Pakistan

关键词: Adomian decomposition method (ADM);    Mittag-Leffler function;    Padé approximation;    Riccati equation;   

DOI  :  10.1186/1687-1847-2013-185

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The aim of this article is to introduce the Laplace-Adomian-Padé method (LAPM) to the Riccati differential equation of fractional order. This method presents accurate and reliable results and has a great perfection in the Adomian decomposition method (ADM) truncated series solution which diverges promptly as the applicable domain increases. The approximate solutions are obtained in a broad range of the problem domain and are compared with the generalized Euler method (GEM). The comparison shows a precise agreement between the results, the applicable one of which needs fewer computations.

【 授权许可】

CC BY