Numerical and Computational Methods
A section of Fractal and Fractional (ISSN 2504-3110).
Section Information
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.
Keywords
- 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.
Editorial Board
Topical Advisory Panel
Special Issues
Following special issues within this section are currently open for submissions:
- Recent Advances in the Spatial and Temporal Discretizations of Fractional PDEs (Deadline: 31 July 2024)
- Theoretical Analysis and Numerical Simulation for Fractional Dynamics and Fractional Calculus (Deadline: 15 August 2024)
- Numerical Solutions of Caputo-Type Fractional Differential Equations and Derivatives (Deadline: 31 August 2024)
- Fractal Dynamics and Machine Learning in Financial Markets (Deadline: 30 September 2024)
- Fractional Mathematical Modelling: Theory, Methods and Applications (Deadline: 30 September 2024)
- Advances in Fractional Modeling and Computation (Deadline: 30 November 2024)
- Advances in Fractional Differential Operators and Their Applications, 2nd Edition (Deadline: 30 November 2024)
- Fractional Diffusion Equations: Numerical Analysis, Modeling and Application, 2nd Edition (Deadline: 30 November 2024)
- Recent Advances in Fractional Differential Equations and Their Applications, 2nd Edition (Deadline: 31 December 2024)
- New Trends on Generalized Fractional Calculus, 2nd Edition (Deadline: 15 January 2025)
- Advances in Fractional Order Derivatives and Their Applications, 3rd Edition (Deadline: 20 March 2025)
- Advanced Numerical Methods for Fractional Functional Models (Deadline: 30 April 2025)
- Numerical Analysis and Iterative Methods for Fractional Differential Equations (Deadline: 13 June 2025)