Fractional Operators and Symmetries in Mathematical Physics

Dear Colleagues,

Fractional calculation appears as a generalization of the derivative of integer order in order to obtain more general results when applied to modeling natural phenomena and real problems, represented in this case by fractional differential equations, that is, differential equations involving fractional derivatives and integrals. These fractional operators have as contributions to the mathematical model the so-called memory effects and non-local effects. As a methodology to study these, we can use analytical methods or numerical methods. If they are linear, we can use the integral transform methodology, in which the type of transformation depends on the type of problem investigated. However, for nonlinear equations, the approach using numerical methods has been seen quite often, but with its limitations. What has enabled a very interesting approach and is already known in the study of nonlinear differential equations in the case of integer order is the theory of Lie group transformations. This has been employed in the field of fractional calculus, providing important results, especially when obtaining invariant solutions via Lie symmetries or order reductions in the studied equations.

This Special Issue is devoted to new developments in the theory of Lie symmetries applied to fractional differential equations,  having as main objectives the Lie symmetries for fractional models, used both to reduce the differential equations investigated and to obtain their analytical or numerical solutions. Another motivation is the investigation of this theory, considering the geometric aspects, in which we can cite the main result, the conservation law involved. 

Prof. Dr. Felix Silva Costa
Prof. Dr. Gastão Silves Ferreira Frederico
Guest Editors

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