Abstract
We consider fractional derivatives of a Colombeau generalized stochastic process G defined on ℝn. We first introduce the Caputo fractional derivative of a one-dimensional Colombeau generalized stochastic process and then generalize the procedure to the Caputo partial fractional derivatives of a multidimensional Colombeau generalized stochastic process. To do so, the Colombeau generalized stochastic process G has to have a compact support. We prove that an arbitrary Caputo partial fractional derivative of a compactly supported Colombeau generalized stochastic process is a Colombeau generalized stochastic process itself, but not necessarily with a compact support.
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Rajter-Ćirić, D., Stojanović, M. Fractional derivatives of multidimensional Colombeau generalized stochastic processes. fcaa 16, 949–961 (2013). https://doi.org/10.2478/s13540-013-0058-z
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DOI: https://doi.org/10.2478/s13540-013-0058-z