In this paper, we study local and nonlocal boundary value problems for hyperbolic equations of general form with variable coefficients and a Caputo fractional derivative. To study the stated problem, a certain fractional-order functional space is introduced. The problem posed is reduced to an integral equation, and the existence of its solution is proved using an a priori estimate.

中文翻译：

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具有 Caputo 分数阶导数的双曲方程的非局部边值问题

在本文中，我们研究了具有可变系数和 Caputo 分数阶导数的一般形式的双曲方程的局部和非局部边值问题。为了研究上述问题，引入了某个分数阶泛函空间。提出的问题简化为一个积分方程，并使用先验估计证明其解的存在性。