中文摘要：

分数阶导数是整数阶导数的推广．近年来分数阶导数已经成为描述各类复杂力学与物理过程的重要工具．与经典的整数阶导数相比，分数阶导数具有历史记忆性和全域相关性，能较好地体现系统函数的演化过程．相对于非线性模型而言，分数阶模型的物理意义更清晰，表述更简洁、准确．本文讨论两类分数阶双曲型偏微分方程正、反问题的适定性，并利用适定性构造了一个加密算法．

英文摘要：

The fractional derivative is a generalization of the integer order derivative. In recent years, the fractional derivative has become an important description tool for all kinds of complex mechanisms and physical processes. Compared with the classical integer order derivative, historical memory and the global correlation of fractional order derivative make it more suitable for describing the evolution of a system. Moreover, relative to the nonlinear models, the physics significance of fractional order model is more clear, concise and accurate. This paper discusses the well-posedness problem of two types of fractional order hyperbolic partial differential equations, and constructs an encryption algorithm based on the well-posedness.