Trends in Fractional Modelling in Science and Innovative Technologies
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".
Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 12187
Special Issue Editor
Interests: non-linear transport phenomena; modelling; scaling; fractional calculus; heat and mass transfer; diffusion problems
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Fractional calculus has played an important role in the fields of mathematics, physics, electronics, mechanics, and engineering in recent years. Modelling methods involving fractional operators are being continuously generalized and enhanced, especially during the last few decades.
Fractional calculus has an amazing history in the modelling of non-linear and anomalous problems in mathematics, physics, statistics, and engineering, involving a diversity of fractional-order integral and derivative operators, such as the ones named after Grunwald–Letnikov, Riemann–Liouville, Weyl, Caputo, Hadamard, Riesz, Erdelyi–Kober, etc. based on the power-law memory. Beyond this positive classical basis, in recent years new trends in fractional modelling involving operators with non-singular kernels were created to model dissipative phenomena that cannot be adequately modelled by fractional differential operators based on singular kernels.
The goal of this Special Issue is to report the latest progress in fractional calculus oriented towards scientific and engineering problems in the light of the classic (power-law) and modern trends (with non-singular kernels) thus allowing the scientific society to see what could be done and how in this amazing area of mathematical modelling.
We kindly invite researchers working within the fields of theory, methods, and applications of these problems to submit their latest findings to this Special Issue.
The main topics of the collection include, but are not limited to:
- Fractional modelling: broad aspects;
- Solution techniques: analytical and numerical;
- Fractional modelling: new trends, new fractional operators, mathematical properties of fractional operators;
- Fractional-order ODEs, PDEs, and integro-differential equations involving new fractional operators;
- Memory kernels to fractional operators: identification, construction, definitions of fractional operators on their basis and relevant properties;
- Special functions of mathematical physics and applied mathematics associated with classical and new fractional operators;
- Examples beyond the classical singular kernel applications: Non-power-law relaxations involving new operators;
- Symmetry in fractional operators and models;
- Thermodynamic compatibility of fractional models with singular and nonsingular kernels;
- Diffusion models: broad aspects;
- Local fractional calculus;
- Discrete fractional calculus;
- Heat, mass, and momentum transfer (fluid dynamics) with relaxations (power-law and bounded kernels);
- Mechanics and rheology of solid materials and innovative fractional modelling;
- Nano-applications of fractional modelling;
- Biomechanical and biomedical applications of fractional calculus;
- Chaos and complexity;
- Control problems and model identifications with singular and non-singular fractional operators;
- Electrochemical systems and alternative energy sources: models by fractional operators;
- Fractional modelling of electrochemical and magnetic systems;
- Dynamical and stochastic systems based upon fractional calculus with singular and non-singular fractional operators.
Prof. Dr. Jordan Hristov
Guest Editor
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