Solutions to Some Fractional Differential Equations and Their Integrable Discretizations

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Abstract

Two linear fractional differential equations appearing in the field of fluid mechanics are investigated. These equations are solved by employing a Puiseux expansion and their solutions are expressed in terms of the Mittag–Leffler function. Ordinary differential equations without fractional derivatives that the fundamental solutions satisfy are also derived. We also present an integrable discretization of the fractional differential equation together with its solution.

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