| Summary: | In this paper we study the time-fractional wave equation of order <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo><</mo> <mi>ν</mi> <mo><</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> and give a probabilistic interpretation of its solution. In the case <inline-formula> <math display="inline"> <semantics> <mrow> <mn>0</mn> <mo><</mo> <mi>ν</mi> <mo><</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>, the solution can be interpreted as a time-changed Brownian motion, while for <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo><</mo> <mi>ν</mi> <mo><</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> it coincides with the density of a symmetric stable process of order <inline-formula> <math display="inline"> <semantics> <mrow> <mn>2</mn> <mo>/</mo> <mi>ν</mi> </mrow> </semantics> </math> </inline-formula>. We give here an interpretation of the fractional wave equation for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>></mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> in terms of laws of stable <i>d</i>−dimensional processes. We give a hint at the case of a fractional wave equation for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>ν</mi> <mo>></mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> and also at space-time fractional wave equations.
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