A FOUNDATIONAL APPROACH TO THE LIE THEORY FOR FRACTIONAL ORDER PARTIAL DIFFERENTIAL EQUATIONS

作者：Leo Rosario Antonio^*; Sicuro Gabriele; Tempesta Piergiulio

来源：Fractional Calculus and Applied Analysis, 2017, 20(1): 212-231.

DOI：10.1515/fca-2017-0011

• fractional calculus
• Riemann-Liouville fractional operator
• fractional ordinary and partial differential equations
• Lie theory
• symmetries

We provide a general theoretical framework allowing us to extend the classical Lie theory for partial differential equations to the case of equations of fractional order. We propose a general prolongation formula for the study of Lie symmetries in the case of an arbitrary finite number of independent variables. We also prove the Lie theorem in the case of fractional differential equations, showing that the proper space for the analysis of these symmetries is the infinite dimensional jet space.

• 出版日期2017-2