A generalized analytical approach for highly accurate solutions of fractional differential equations

被引:4
|
作者
Xu, Hang [1 ]
机构
[1] Shanghai Jiao Tong Univ, Sch Naval Architecture Ocean & Civil Engn, State Key Lab Ocean Engn, Shanghai 200240, Peoples R China
基金
中国国家自然科学基金;
关键词
Fractional differential equation; Analytical approximation; Arbitrary accuracy; Scaling transformation; NUMERICAL-SOLUTIONS; DIFFUSION EQUATION;
D O I
10.1016/j.chaos.2022.112917
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A generalized homotopy-based approach is developed to give highly accurate solutions of fractional differential equations. By introducing a scaling transformation, the computational domain of the nonlinear Riccati differ-ential equations with fractional order changes from [0,+infinity) to [0,1]. Analytical approximation of arbitrary ac-curacy is achieved, whose convergence is proved theoretically. The effectiveness and accuracy of our solution is strictly checked via error analysis. The proposed method is expected to be as a new and reliable analytical approach to give highly accurate solutions of strongly nonlinear problems in fractional calculus.
引用
收藏
页数:6
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