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A generalisation of the Malgrange-Ehrenpreis theorem to find fundamental solutions to fractional PDEs

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Date

2017

Authors

Baleanu, Dumitru
Fernandez, Arran

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Univ Szeged, Bolyai Institute

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Abstract

We present and prove a new generalisation of the Malgrange-Ehrenpreis theorem to fractional partial differential equations, which can be used to construct fundamental solutions to all partial differential operators of rational order and many of arbitrary real order. We demonstrate with some examples and mention a few possible applications.

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Fractional Derivatives, Fundamental Solutions, Linear Partial Differential Equations, Constructive Solutions

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Baleanu, Dumitru; Fernandez, Arran (2017). A generalisation of the Malgrange-Ehrenpreis theorem to find fundamental solutions to fractional PDEs, Electronic Journal Of Qualitative Theory Of Differential Equations, 15, 1-12

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Electronic Journal Of Qualitative Theory Of Differential Equations

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15

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1

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12