作 者: ;
机构地区: 华南理工大学理学院数学与应用数学系
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
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.