Theory and Applications of Fractional Differential Equations

This monograph provides the most recent data on fractional calculations.

Subject subject numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous numerous. widespread fields of science and engineering.

Application of Fluid Flow, Solute Transport, or Dynamical Processes in Self-Similar and Structural Structures, Diffusive Transport akin to Diffusion, Material Viscoelastic Theory, Electromagnetic Theory, Dynamics of Earthquakes, Control Theory of Dynamical Systems, Optics and Signal Processing, Bio-Sciences, Economics, Geology, Astrophysics, Probability and Statistics, Chemical Physics, and so on.

In the above-mentioned areas, there are phenomena with classical kinetics which have a microscopic complex behavior, and their macroscopic dynamics.

The fractional order equals 1/3, or square root of 2, and so on. Some of dry fractional models can have solutions. Weierstrass type functions. Such kinds of properties are, obviously, impossible for the ordinary models.

What are the useful properties for these anomalous processes? From the point of view of experimental results, have a long-term experience in the field of non-local dynamics.

I am interested in mathematical, physical, and other science sciences, who are not interested in mathematics and other applications. fractional differential equations, but also in further investigations.

This monograph consists of a total of eight chapters and a very extensive bibliography. The main objective is to write a summary of the problem. The aim of the problem is to find a way to solve the problems of the problem. Methods, closed-form solutions of ordinary and partial differential equations, and the theory of the developed theory.

Key features:

- It is mainly application oriented.
- It contains a complete theory of Fractional Differential Equations.
- It can be used as a postgraduate-level textbook in many different disciplines within science and engineering.
- It contains an up-to-date bibliography.
- It provides problems and directions for further investigations.
- Fractional Modeling is an emerging field of science and engineering.
- It contains many examples.
- and so on!

1. Preliminaries.
2. Fractional Integrals and Fractional Derivatives.
3. Ordinary Fractional Differential Equations. Existence and Uniqueness Theorems.
4. Methods for Explicitly solving Fractional Differential Equations.
5. Integral Transform Methods for Explicit Solutions is Fractional Differential Equations.
6. Partial Fractional Differential Equations.
7. Sequential Linear Differential Equations of Fractional Order.
8. Further Applications of Fractional Models.
Bibliography
Subject Index