Modelling Problems Arising in Science and Engineering with Fractional Differential Operators: Beyond the Power-Law Limit

Dear Colleagues,

You are kindly invited to contribute to the Special Issue “Modelling Problems Arising in Science and Engineering with Fractional Differential Operators: Beyond the Power-Law Limit”.

Fractional calculus has a brilliant history in the modelling of non-linear and anomalous problems in mathematics, physics, statistics and engineering, involving a variety 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 bright classical basis, in recent years new trends in fractional modelling involving operators with non-singular kernels have been created to model dissipative phenomena that cannot be adequately modelled by fractional differential operators based on singular kernels.

This Special Issue addresses contemporary modeling problems in science and engineering involving fractional differential operators with classical and new memory kernels. This is a call to authors involved in modeling with new and classical fractional differential operators to show their important positions in fractional modelling theory, differences in applications and how these operators should be applied. The issue offers a broad range of applied topics and multidisciplinary applications of fractional order differential operators with classical and new kernels in science and engineering.

We invite and welcome review, expository, and original research articles dealing with recent advances in the theory of fractional-order integral and derivative operators and their multidisciplinary applications. We will be glad to see your contributions with strong results demonstrating the feasibility of both the classical and the new trends in fractional calculus.

The main topics of the collections envisage some principle problems, including but not limited to:

• Fractional modelling: new trends, new fractional operators, mathematical properties of fractional operators,
• Memory kernels to fractional operators: identification, construction, definitions of fractional operators on their basis and relevant properties
• Fractional-order ODEs, PDEs and integro-differential equations involving new fractional operators
• Special functions of mathematical physics and applied mathematics associated with the new fractional operators
• Examples beyond the classical singular kernel applications: Non-power-law relaxations involving new operators
• Fractional modelling of the mechanics and rheology of solid materials with non-power-law relaxations
• Anomalous diffusion models beyond the power-law behaviour
• Fractional modelling for biomechanical and biomedical applications with new operators
• Thermodynamic compatibility of fractional models with new kernels
• Fractional models of heat, mass and fluid flow beyond the power-law
• Control and signal fractional modelling problems with non-singular fractional operators
• Dynamic and stochastic systems based on fractional calculus with non-power-law kernels
• Fractional modelling of electrochemical and magnetic systems with non-singular operators

Prof. Dr. Jordan Hristov
Guest Editor

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