Description
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.- Provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines- Presents a systematic introduction to most of the important special functions in Fractional Calculus that commonly arise in scientific and engineering practice- Explores many salient computational modeling properties- Analyzes theoretical and practical problems in Fractional Calculus in fields such as Engineering, Computer Science, Management, Social Science, and the Humanities
Table of Contents
1. Special Functions of the Fractional Calculus2. Fractional Derivatives and Integrals3. Transforms of Fractional Derivatives4. Linear Fractional Differential Equations5. Fractional Green's Function6. Other Methods for the Solution of Fractional-order Equations7. Fractional ordinary differential equations and properties8. Existence and uniqueness of solutions to Cauchy-type problems9. Stability estimates for fractional order differential equations10. Partial Fractional differential equations and their solutions11. Numerical Evaluation of Fractional Derivative12. Approximation of Fractional Derivatives13. Numerical method for fractional order ordinary differential equations14. Finite-difference method for fractional ODEs15. High-order approximation of Caputo fractional derivative16. Adaptive and high-order scheme for non-integer order differential equations17. Time-fractional diffusion equations18. Fractional diffusion19. Fractional‐order Modeling20. Linear Fractional‐order Systems21. Current trends in fractional derivatives22. Fractional‐order Control23. Fractional integral inequalities and Applications24. Discrete fractional calculus and applications25. Fractional variational calculus and fractional Euler-Lagrange Equation26. Fractional Calculus in Image/Signal Processing
