Recent Developments in Theory and Applications of Fractional Order Systems presents a rigorous and thorough analysis of various aspects of Fractional Calculus. The book provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines. The authors present each computational modeling concept with a definition, methods, theorems, and observations followed by typical application problems and step-by-step solutions. Each topic is covered in detail, followed typically by several meticulously worked out examples and a problem set containing many additional related problems.
In addition, the book discusses recent developments and the latest research on Fractional Calculus and its applications, demonstrating important applications in Engineering, Computer Science, Management, Social Science, and the Humanities.
1. Special Functions of the Fractional Calculus
2. Fractional Derivatives and Integrals
3. Transforms of Fractional Derivatives
4. Linear Fractional Differential Equations
5. Fractional Green's Function
6. Other Methods for the Solution of Fractional-order Equations
7. Fractional ordinary differential equations and properties
8. Existence and uniqueness of solutions to Cauchy-type problems
9. Stability estimates for fractional order differential equations
10. Partial Fractional differential equations and their solutions
11. Numerical Evaluation of Fractional Derivative
12. Approximation of Fractional Derivatives
13. Numerical method for fractional order ordinary differential equations
14. Finite-difference method for fractional ODEs
15. High-order approximation of Caputo fractional derivative
16. Adaptive and high-order scheme for non-integer order differential equations
17. Time-fractional diffusion equations
18. Fractional diffusion
19. Fractional‐order Modeling
20. Linear Fractional‐order Systems
21. Current trends in fractional derivatives
22. Fractional‐order Control
23. Fractional integral inequalities and Applications
24. Discrete fractional calculus and applications
25. Fractional variational calculus and fractional Euler-Lagrange Equation
26. Fractional Calculus in Image/Signal Processing
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