Fractal and Fractional
Scope & Guideline
Innovative Research at the Intersection of Fractals and Calculus
Introduction
Aims and Scopes
- Fractional Calculus Applications:
The journal emphasizes studies involving fractional calculus, which includes its applications in modeling dynamic systems across physics, engineering, and biology. This includes fractional differential equations and their solutions. - Fractal Geometry and Its Applications:
Research on fractal geometry is a core aspect of the journal, with papers discussing the mathematical properties of fractals and their applications in various fields such as materials science, ecology, and computer graphics. - Modeling and Simulation:
The journal publishes works that apply fractional and fractal models to real-world phenomena, including simulations of physical processes, financial modeling, and biological systems. - Interdisciplinary Research:
The journal encourages interdisciplinary studies that integrate concepts from mathematics, physics, engineering, and computer science, showcasing how fractal and fractional theories can solve complex problems in diverse fields. - Numerical Methods and Computational Techniques:
A significant focus is on the development and application of numerical methods for solving fractional and fractal problems, including innovative algorithms and computational techniques.
Trending and Emerging
- Integration of Machine Learning and AI:
An increasing number of papers are exploring the application of machine learning and artificial intelligence in conjunction with fractal and fractional modeling, particularly for predictive analytics and optimization. - Environmental and Ecological Applications:
Research focusing on environmental modeling, including climate change effects and ecological dynamics using fractal and fractional approaches, has gained significant traction. - Complex Systems and Network Theory:
There is a growing interest in applying fractal and fractional concepts to complex systems and network theories, particularly in understanding phenomena in social sciences, economics, and biology. - Advanced Numerical Techniques:
Emerging methodologies in numerical analysis and computational techniques for solving complex fractional and fractal equations are becoming a focal point, emphasizing the importance of efficient algorithms. - Hybrid Models:
The development of hybrid models that combine fractional calculus with other mathematical frameworks, such as fuzzy logic or stochastic processes, is becoming increasingly popular.
Declining or Waning
- Basic Theoretical Developments:
There has been a noticeable shift away from purely theoretical discussions of fractals and fractional calculus towards more applied research and interdisciplinary applications. - Traditional Applications of Fractals:
Applications of fractals in traditional fields such as pure mathematics and theoretical physics have seen a decrease in favor of more practical applications in engineering and technology. - Static Models:
Research focusing on static models that do not consider dynamic interactions or time-dependent behaviors has become less prominent compared to studies involving dynamic systems and their complexities.
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