分数階微積分学とその応用における最新の潮流 Recent Trends in Fractional Calculus and Its Applications (Advanced Studies in Complex Systems)

Agarwal, Praveen (EDT)/ Martínez, Luis Vázquez (EDT)/ Lenzi, Ervin K. (EDT)

Academic Press Inc（2024/07発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 300 p.
• 言語 ENG
• 商品コード 9780443185052
• DDC分類 515.83

Full Description

Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics.

The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences.

Contents

1. New Directions in Fractional Differential Equations
2. On Riesz Derivative Problems
3. Some Proposals for a Renewal in the Field of Fractional Behaviour Studies
4. The Origin of the Generalized Memory: Analysis of the Balance Equations and Corrections to Newton's 3rd Law
5. Modeling COVID-19 Pandemic Outbreak Using Fractional-Order Systems
6. Damage and Fatigue Described by a Fractional Model
7. Wavelet Fractional Operators
8. Fractional Calculus Applied to Image Processing
9. Dynamics, Simulation and Parameter Estimation of a Fractional Incommensurate Model Predicting Covid-19
10. Fractional Calculus and Its Applications to Biology
11. Fractional Differential Equations and its Applications in Circuits Theory
12. Fractional Calculus: A Reliable Tool for Solving Real World Problems
13. Approximation of Mild Solutions of a Semilinear Fractional Differential Equation
14. Extended Fractional Calculus
15. Fractional Calculi on Time Scales