A fractional order variant of the Delsarte equation is investigated involving the Caputo differential derivative. Solvability of the resulting fractional hyperbolic Cauchy problem is achieved in the sense of distributions. A regularity result shows that the solution may be a function of time. Rigorous Delsarte representations are established. The symmetry between the fractional operators acting on space and time, induced by the Delsarte equation, opens the door to new type of fractional partial differential equations.

中文翻译：

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分数阶微积分 Caputo 算子的 Delsarte 方程

Delsarte 方程的分数阶变体被研究涉及 Caputo 微分导数。由此产生的分数双曲柯西问题的可解性是在分布的意义上实现的。规律性结果表明解可能是时间的函数。建立了严格的 Delsarte 表示。由 Delsarte 方程引起的作用于空间和时间的分数算子之间的对称性为新型分数偏微分方程打开了大门。