分数阶Laguerre型电报方程的解析解  

Analytical Solutions of Fractional Laguerre Telegraph Equation

作　　者：陈阳 胡越[2] 

机构地区：[1]郑州工业应用技术学院基础教学部,河南新郑451100 [2]河南理工大学数学与信息科学学院,河南焦作454000

出　　处：《河北北方学院学报（自然科学版）》2017年第3期22-29,共8页Journal of Hebei North University:Natural Science Edition

摘　　要：目的针对一类特殊的分数阶电报方程——Laguerre型分数阶电报方程,拟通过不同求解方法分析其解的级数形式,为有效解决分数阶微分方程近似解提供便利求解方法。方法以Laguerre型分数阶电报方程为研究对象,通过同伦摄动、Adomian分解法、变分迭代法、各种积分变换法、算子方法及同伦分析法等研究方法,分析Laguerre型分数阶电报方程解的具体形式。通过深入研究各种方法的优缺点,发现利用算子方法可以构建带初边值条件的时间(空间)分数阶电报方程的解的结构。结果给出了Laguerre型分数阶电报方程不同初边值形式下的4个定理,分别给出对应形式下解的结构,结合具体定理的运算过程充分证明解的结构的正确性。结论采用算子方法可以有效求解分数阶Laguerre型电报方程的解析解,且具有准确性高的特点,为此类问题的求解方法提供科学指导。Objective For a special class of fractional telegraph equations—Laguerre type fractional telegraph equation,the solution in the form of a series of different solving methods was discussed to solve approximate solution of fractional differential equations.Methods Using moving homotopy perturbation method,Adomian decomposition method,variational iteration method,various integral transform method,operator method,homotopy analysis method and other research methods to analyze the specific form of the solution Laguerre fractional telegraph equation.By in-depth studying the advantages and disadvantages of each method,the operator method was found to be used to build the structure of the solution time boundary conditions with time-(space-)fractional telegraph equation.Results Four different theorems about initial and boundary Laguerre fractional telegraph equation were given corresponding the form of solutions structure,and proved the solutions structure in combination with the specific process theorems.Conclusions By using the method,operators can effectively solve the analytical solution of Laguerre telegraph equation.So the method has the characteristics of high accuracy and provides scientific guidance to solving such problems.

关 键 词：算子方法 分数阶电报方程 Riemann-Liouville分数阶导数 CAPUTO分数阶导数 

分 类 号：O175[理学—数学]