This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics and applications.
The information in the book is presented in four parts:
- Fractional Diffusion Equations: (i) solutions of fractional diffusion equations using wavelet methods, (ii) the maximum principle for time fractional diffusion equations, (iii) nonlinear sub-diffusion equations.
- Mathematical Analysis: (i) shifted Jacobi polynomials for solving and identifying coupled fractional delay differential equations, (ii) the monotone iteration principle in the theory of Hadamard fractional delay differential equations, (iii) dynamics of fractional order modified Bhalekar-Gejji System, (iv) Grunwald-Letnikov derivatives.
- Computational Techniques: GPU computing of special mathematical functions used in fractional calculus.
- Reviews: (i) the popular iterative method NIM, (ii) fractional derivative with non-singular kernels, (iii) some open problems in fractional order nonlinear system
This is a useful reference for researchers and graduate level mathematics students seeking knowledge about of fractional calculus and applied mathematics.
3. List of Contributors
4. Solving Fractional Diffusion Equation by Wavelet Methods
5. A Survey on the Recent Results Regarding Maximum Principles for the Time-Fractional Diffusion Equations
6. Integral-Balance Solution to Nonlinear Subdiffusion Equation
7. Analysis of Solution and System Identification of Coupled Fractional Delay Differential Equation by Shifted Jacobi Polynomials
8. Dynamics of Fractional Order Modified Bhalekar- Gejji System
9. Grunwald-Letnikov Derivative: Analysis in Range of First Order
10. GPU Computing of Special Mathematical Functions used in Fractional Calculus
11. New Iterative Method: A Review
12. Derivatives with Non-Singular Kernels from the Caputo-Fabrizio Definition and Beyond: Appraising Analysis with Emphasis on Diffusion Models
13. Fractional Order Nonlinear Systems: Some Open Problems in Numerical Computations and Chaos Theory
14. Subject Index