Numerical and Computational Methods

Fractional calculus is emerging as an adequate methodology for describing many physical phenomena and controlling systems of both integer and non-integer order. The additional degrees of freedom provided by the non-integer order and the ability to describe memory effects in system dynamics are among the main characteristics of a such successful approach.

An effective approach to validate the effectiveness and applicability of non-integer order systems is the development of Numerical and Computational Methods specifically devoted to solve fractional order problems.

The aim of this Section in Fractal and Fractional is therefore to enable the efficacy of fractional calculus to be confirmed and to propose the implementation of new numerical and computational methods based also on fractional calculus and non integer classical methods. Relevant original applications are also welcome. The range of the applications is very wide; including mathematicians/physicists (with possible implementations by a suitable computer software like e.g. MatLab, Mathematica, ...), material engineers (with possible implementations in Ansys, Comsol, ..), electronic engineers (with possible implementations in Spice, Cadence, ..) and control engineers (with possible implementations on microcontrollers).

Authors are encouraged to submit both research and applicative papers proposing and comparing new numerical and computational methods based on fractional calculus and relevant applications.

• fractional calculus;
• numerical methods;
• approximation methods;
• computational procedures;
• algorithms;
• digital implementation;
• hardware in the Loop implementation;
• FPGA implementation;
• data mining with fractional calculus methods;
• fractional calculus with artificial intelligence applications;
• image/signal analyses based on fractional calculus;
• fuzzy fractional calculus;
• neural computations with fractional calculus;
• applications of fractional calculus in nonlinear science;
• applications in control, mechanics, financial mathematics, engineering, biomedecine, etc.