有限区间上的时间分数阶电报方程的解析解  

ANALYTIC SOLUTIONS FOR THE TIME-FRACTIONAL TELEGRAPH EQUATION DEFINED IN A BOUNDED DOMAIN

作　　者：黄凤辉[1] 

机构地区：[1]华南理工大学理学院数学系,广东广州510641

出　　处：《华南师范大学学报（自然科学版）》2010年第1期15-19,共5页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金数学天元基金资助项目(10726061);国家教育部高等学校博士点基金新教师基金资助项目(20070561040);广东省自然科学基金资助项目(07300823)

摘　　要：考虑一类时间分数阶电报方程,它是由传统的电报方程推广而来,即时间一阶、二阶导数分别用α(1/2,1],2α(1,2]阶Caputo导数代替.利用空间有限的sine或cosine变换及时间Laplace变换,给出了该方程有限区间上带Dirichlet和Neumann边界条件的两类初边值问题的解析解.该解由Mittag-Leffler函数的级数形式给出.The so-called time-fractional telegraph equation is discussed.It is a generalization of the classical telegraph equation in case the first-and two-order time derivatives are replaced with Caputo derivatives of order α（12,1],2α（1,2].By using the spatial finite sine and cosine transform,and the temporal Laplace transform,the existence of the analytic solutions of its initial-boundary problems in a boundedspace domain with Dirichlet and Neumann boundary conditions is derived.The analytic solutions are given in the form of series of the Mittag-Leffler functions.

关 键 词：分数阶电报方程 CAPUTO分数阶导数 sine(cosine)变换 LAPLACE变换 

分 类 号：O175.2[理学—数学]