Computation and modeling for fractional order systems /

Computation and Modeling for Fractional Order Systems provides readers with problem-solving techniques for obtaining exact and/or approximate solutions of governing equations arising in fractional dynamical systems presented using various analytical, semi-analytical, and numerical methods. In this r...

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Bibliographic Details
Corporate Author:	ScienceDirect (Online service)
Other Authors:	Chakraverty, Snehashish (Editor), Jena, Rajarama Mohan (Editor)
Format:	eBook
Language:	English
Published:	London : Academic Press, 2024.
Subjects:	Fractional differential equations. Fractional calculus. Dérivées fractionnaires. Équations différentielles fractionnaires. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Front Cover
Computation and Modeling for Fractional Order Systems
Copyright
Contents
List of contributors
1 Response time and accuracy modeling through the lens of fractional dynamics
1.1 Introduction
1.1.1 Historical foundation and applications of sequential sampling theory
1.1.2 Lévy flight models as an extension of diffusion models
1.2 Lévy-Brownian model as a model with both Lévy and diffusion properties
1.3 A tutorial on how to fit the Lévy-Brownian model
1.3.1 First-passage time approximation
1.3.2 Likelihood construction
1.4 Fitting to experimental data
1.5 Discussion
1.6 Conclusion
References
2 An efficient analytical method for the fractional order Sharma-Tasso-Olever equation by means of the Caputo-Fabrizio deriv...
2.1 Introduction
2.2 Progress of fractional derivatives in the absence of singular kernel
2.3 Fundamental scheme of the modified form of HATM with new derivative
2.4 Analysis of MHATM with Caputo-Fabrizio derivative
2.5 Numerical solution of the time-fractional STO equation
2.5.1 Numerical discussion
3.2.3.1 Diffusion-flux relationship: the fading memory concept
3.2.3.2 Boltzmann's superposition
3.2.3.3 Simple heat conduction example: Cattaneo's approach
3.2.3.4 Extended fading memory concept
3.3 Kernel effects on the constitutive equations
3.3.1 Caputo type fractional operators: the general concept
3.3.1.1 Example 1: exponential memory
3.3.1.2 Example 2: Mittag-Leffler (one-parameter) memory
3.3.1.3 Example 3: Prabhakar memory kernel
3.3.1.4 Example 4: Rabotnov kernel as a memory
3.3.2 Volterra equation approach
3.3.2.1 The concept and Riemann-Liouville operators
3.3.2.2 Example 5: exponential memory
3.3.2.3 Example 6: Mittag-Leffler (one-parameter) function as a kernel
3.3.2.4 Example 7: Prabhakar kernel as a memory
3.3.2.5 Example 8: Rabotnov kernel as a memory
3.4 Final comments and outcomes
Appendix 3.A Mittag-Leffler functions and fractional operators
3.A.1 Mittag-Leffler functions and related kernels
3.A.1.1 One-parameter Mittag-Leffler function
3.A.1.2 Two-parameter Mittag-Leffler function
3.A.1.3 Three-parameter Mittag-Leffler function
3.A.1.4 Prabhakar kernel