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arXiv · 1808.06803

The fractional d'Alembert's formulas

Cheng-Gang Li·Miao Li·Sergey Piskarev·Mark M. Meerschaert
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Abstract

In this paper we develop generalized d'Alembert's formulas for abstract fractional integro-differential equations and fractional differential equations on Banach spaces. Some examples are given to illustrate our abstract results, and the probability interpretation of these fractional d'Alembert's formulas are also given. Moreover, we also provide d'Alembert's formulas for abstract fractional telegraph equations.

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Cheng-Gang Li, Miao Li, Sergey Piskarev, Mark M. Meerschaert. 2018-08-21. The fractional d'Alembert's formulas. https://arxiv.org/abs/1808.06803

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