A Fractional Variational Approach to the Fractional Basset-Type Equation

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• 作者：Dumitru Baleanu ; Roberto Garra ; Ivo Petras
• 关键词：Basset equation ; fractional calculus ; calculus of variations
• 刊名：Reports on Mathematical Physics
• 出版年：August, 2013
• 年：2013
• 卷：72
• 期：1
• 页码：57-64
• 全文大小：125 K

文摘

In this paper we discuss an application of fractional variational calculus to the Basset-type fractional equations. It is well known that the unsteady motion of a sphere immersed in a Stokes fluid is described by an integro-differential equation involving derivative of real order. Here we study the inverse problem, i.e. we consider the problem from a Lagrangian point of view in the framework of fractional variational calculus. In this way we find an application of fractional variational methods to a classical physical model, finding a Basset-type fractional equation starting from a Lagrangian depending on derivatives of fractional order.