In this article, we have studied solutions of a generalised multiorder fractional partial differential equations involving the Caputo time-fractional derivative and the Riemann–Liouville space fractional derivatives using Laplace–Fourier transform technique. Proposed generalised multiorder fractional partial differential equation is reducible to Schrödinger equation, wave equation and diffusion equation in a more general sense, and hence, solutions of these equations are specifically noted. Not only this, solutions of equation proposed in the stochastic resetting theory in the context of Brownian motion can also be found in a general regime.

中文翻译：

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关于物理学中广义多阶分数阶偏微分方程的解

在本文中，我们使用拉普拉斯-傅立叶变换技术研究了涉及 Caputo 时间分数阶导数和 Riemann-Liouville 空间分数阶导数的广义多阶分数阶偏微分方程的解。所提出的广义多阶分数阶偏微分方程在更一般的意义上可简化为薛定谔方程、波动方程和扩散方程，因此，这些方程的解被特别指出。不仅如此，布朗运动背景下的随机重置理论中提出的方程解也可以在一般状态下找到。