Analytic Approximate Solutions for a Class of Variable Order Fractional Differential Equations Using The Polynomial Least Squares Method

被引：0
作者：
Constantin Bota
Bogdan Căruntu
机构：
[1] “Politehnica” University of Timişoara,Dept. of Mathematics
来源：
Fractional Calculus and Applied Analysis | 2017年 / 20卷
关键词：
Primary 26A33; Secondary 34A08; 34E10; 41A10; nonlinear variable order fractional differential equation; approximate analytic polynomial solution; Polynomial Least Squares Method;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper a new way to compute analytic approximate polynomial solutions for a class of nonlinear variable order fractional differential equations is proposed, based on the Polynomial Least Squares Method (PLSM). In order to emphasize the accuracy and the efficiency of the method several examples are included.
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页码：1043 / 1050
页数：7
相关论文
共 31 条
[1]  
Atanackovic TM(2011)Hamilton’s principle with variable order fractional derivatives Fract. Calc. Appl. Anal 14 94-109
[2]  
Pilipovic S(2013)A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures Fract. Calc. Appl. Anal 16 76-92
[3]  
Chen W(2015)Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets Appl. Math. Lett 46 83-88
[4]  
Zhang JJ(2004)Filtering using variable order vertical derivatives Comput. Geosci 30 455-459
[5]  
Zhang JY(2012)A reproducing kernel method for solving nonlocal fractional boundary value problems Appl. Math. Lett 25 818-823
[6]  
Chen YM(2005)Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions Differ. Equ 1141 84-89
[7]  
Wei YQ(2008)Basic theory of fractional differential equations Nonlinear Anal. TMA 69 2677-2683
[8]  
Liu DY(2015)Approximate analytical solutions of nonlocal fractional boundary value problems Appl. Math. Model 39 1717-1724
[9]  
Yu H(2015)A numerical technique for variable fractional functional boundary value problems Appl. Math. Lett 43 108-113
[10]  
Cooper GRJ(2016)Maximum principles for multi-term space-time variable-order fractional sub-diffusion in concrete structures Fract. Calc. Appl. Anal 19 188-211
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