Nonlocal and Fractional Operators: A Comprehensive Guide

In recent years, nonlocal and fractional operators have gained increasing attention due to their wide applications in various fields such as physics, engineering, and finance. These operators offer a powerful tool for modeling complex phenomena that exhibit long-range interactions, memory effects, and fractal-like behavior.

Nonlocal Operators

Unlike local operators that act on a single point in space or time, nonlocal operators have the ability to affect a wider range of points. They take into account the influences and interactions of neighboring points, thereby capturing nonlocality or long-range correlations.

Nonlocal and Fractional Operators (SEMA SIMAI Springer Series Book 26)

by Roberto Garrappa

4.6 out of 5

Language	:	English
File size	:	9279 KB
Screen Reader	:	Supported
Print length	:	320 pages

FREE

Fractional Operators

Fractional operators are generalizations of classical integer-Free Download operators. They involve fractional derivatives and integrals, which allow for a more flexible and accurate representation of processes that exhibit fractional or non-integer dynamics.

The applications of nonlocal and fractional operators span a diverse range of disciplines, including:

Physics:

• Modeling anomalous diffusion and transport phenomena
• Describing fractional dynamics in complex media
• Analyzing viscoelastic and poroelastic materials

Engineering:

• Simulating wave propagation and scattering
• Designing fractional-Free Download controllers and filters
• Modeling damage and fatigue in materials

Finance:

• Capturing long-range dependencies in financial time series
• Forecasting volatility and risk
• Analyzing option pricing and hedging strategies

• Enhanced Accuracy: Nonlocal and fractional operators provide a more realistic representation of complex systems by considering long-range interactions and fractional dynamics.
• Increased Flexibility: Fractional derivatives and integrals allow for greater flexibility in modeling processes that exhibit non-integer or anomalous behavior.
• Improved Understanding: These operators offer insights into the underlying mechanisms and processes that govern complex phenomena.

"Nonlocal and Fractional Operators" by Sema Simai Springer is a comprehensive guide to this emerging field. The book covers:

• Mathematical Foundations: A detailed to the mathematical concepts and theories of nonlocal and fractional operators.
• Applications: Extensive coverage of the applications of these operators in various disciplines, with real-world examples.
• Numerical Methods: Practical guidance on numerical techniques for solving nonlocal and fractional operator equations.
• Case Studies: Illustrative case studies that demonstrate the effectiveness and versatility of these operators.

This book is an invaluable resource for researchers, practitioners, and students in:

• Applied Mathematics: Provides a comprehensive foundation in nonlocal and fractional operator theory.
• Engineering and Physics: Offers insights into the modeling and analysis of complex systems using these operators.
• Finance: Facilitates the understanding and application of fractional calculus in financial modeling.

By utilizing nonlocal and fractional operators, researchers and practitioners can gain a deeper understanding of complex phenomena, develop more accurate models, and improve the performance of systems in various fields.

Nonlocal and Fractional Operators (SEMA SIMAI Springer Series Book 26)

by Roberto Garrappa

4.6 out of 5

Language	:	English
File size	:	9279 KB
Screen Reader	:	Supported
Print length	:	320 pages

FREE