Fractional Liénard type model of a pipeline within the fractional derivative without singular kernel

Advances in Difference Equations

JF Gmez-Aguilar¹  D Baleanu⁷  H Ypez-Martnez⁸  L Torres⁹  IO Sosa^1,12  JM Reyes^1,15 

[1] CONACYT - Centro Nacional de InvestigacióCONACYT - Instituto de IngenieríDepartment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Cankaya University, Ankara, Turkey;Institute of Space Sciences, Magurele-Bucharest, Romania;Universidad Autóa, Universidad Nacional Autógico Nacional de Mégico, Tecnolón y Desarrollo Tecnolónoma de Ménoma de la Ciudad de México;xico City, México D.F., México, Cuernavaca, México, Mé

关键词: pipelines;    fluid dynamics;    nonlinear oscillators;    Liénard equation;    Laplace homotopy analysis method;    fractional differential coupled equation;   

DOI  :  10.1186/s13662-016-0908-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper presents the procedure to obtain analytical solutions of Liénard type model of a fluid transmission line represented by the Caputo-Fabrizio fractional operator. For such a model, we derive a new approximated analytical solution by using the Laplace homotopy analysis method. Both the efficiency and the accuracy of the method are verified by comparing the obtained solutions with the exact analytical solution. Good agreement between them is confirmed.

【 授权许可】

CC BY