Guest Editors
Prof. Elina Shishkina
Email: shishkina@amm.vsu.ru; ilina_dico@mai.ru
Affiliation: Department of Mathematical and Applied Analysis, Voronezh State University, 394018 Voronezh, Russia
Homepage:
Research Interests: Fractional calculus, Singular operators, Special finctions
Prof. Syed Abbas
Email: abbas@iitmandi.ac.in
Affiliation: School of Mathematical and Stastical Science, Indian Institute of Technology Mandi, Mandi 175005, India
Homepage:
Research Interests: Delay and fractional differential equations, Numerical methods, Population dynamics, Fractal geometry
Prof. Amar Debbouche
Email: amar_debbouche@yahoo.fr
Affiliation: Department of Mathematics, Guelma University, Guelma 24000, Algeria
Homepage:
Research Interests: Fractional dynamic systems, stochastic analysis, control & optimization, mathematical modeling, numerical simulation
Prof. Shakhobiddin Karimov
Email: shaxkarimov@gmail.com
Affiliation: Department of Applied Mathematics and Informatics, Fergana State University (FSU), Murabbiylar Street, 3A, Fergana 150100, Uzbekistan
Homepage:
Research Interests: Fractional differential equations, Transmutation operators, PDE of mixed type
Summary
Fractional equations have gained significant attention in recent years due to their ability to model complex phenomena in various fields of engineering, such as mechanical, electrical, and civil engineering. These can describe non-local and non-integer order behavior of systems. It is not often possible to solve such engineering problem analytically so numerical methods have become essential tools for approximating solutions.
The aim of numerical methods for fractional equations in engineering is to develop and apply efficient and accurate numerical techniques to solve fractional equations that model complex phenomena in various fields of engineering. The scope of these methods is to provide a framework for simulating, analyzing, and optimizing systems that exhibit non-integer order behavior, including: viscoelastic materials, electrical circuits, control systems, stochastic processes, heat transfer, etc.
The primary objectives of numerical methods for fractional equations in engineering are:
1. Numerical Solution
To develop numerical methods that can solve fractional equations.
2. Efficient Computation
To design numerical methods that are computationally efficient, scalable, and can handle large-scale problems.
3. Interdisciplinary Applications
To apply numerical methods for fractional equations to a wide range of engineering disciplines, including mechanical, electrical, civil, and aerospace engineering.
The scope of numerical methods for fractional equations in engineering includes, but is not limited to:
1. Modeling and Simulation
2. Optimization and Control
3. Data Analysis and Interpretation
The key challenges in achieving the aim and scope of numerical methods for fractional equations in engineering include:
1. Handling the mathematical complexity of fractional equations, including the lack of analytical solutions and the need for numerical approximations.
2. Developing numerical methods that are computationally efficient and can handle large-scale problems.
3. Collaborating with experts from various engineering disciplines to develop and apply numerical methods for fractional equations.
Suggested themes shall be listed.
fractional calculus in theoretical physics and mechanics
mathematical modeling of media with memory
viscoelastic models with fractional order operators
Keywords
Fractional derivatives and integrals, nonlocal effects, memory effects, polymeric materials, viscoelastic media, rigid body mechanics, thermodynamics, hydrodynamics
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