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Methods of Mathematical Modelling : Fractional Differential Equations.

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This book features original research articles on the topic of mathematical modelling and fractional differential equations. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in p...

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Bibliographic Details
Corporate Author: Taylor & Francis
Other Authors: Singh, Harendra, Kumar, Devendra, Baleanu, D. (Dumitru)
Format: eBook
Language:English
Published: Milton : CRC Press LLC, 2019.
Series:Mathematics and Its Applications
Subjects:
TECHNOLOGY / Engineering / Industrial
TECHNOLOGY / Manufacturing
MATHEMATICS / Applied
Mathematical models.
Fractional differential equations.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover; Half Title; Series Page; Title Page; Copyright Page; Contents; Preface; Editors; Contributors; 1 Mathematical Analysis and Simulation of Chaotic Tritrophic Ecosystem Using Fractional Derivatives with Mittag-Leffler Kernel; 1.1 Introduction; 1.2 Method of Approximation of Fractional Derivative; 1.3 Model Equations and Stability Analysis; 1.3.1 Fractional Food Chain Dynamics with Holling Type II Functional Response; 1.3.2 Multi-Species Ecosystem with a Beddington-DeAngelis Functional Response; 1.4 Numerical Experiment for Fractional Reaction-Diffusion Ecosystem; 1.5 Conclusion
  • 4 A New Approximation Scheme for Solving Ordinary Differential Equation with Gomez-Atangana-Caputo Fractional Derivative4.1 Introduction; 4.2 A New Numerical Approximation; 4.2.1 Error Estimate; 4.3 Application; 4.3.1 Example 1; 4.3.2 Example 2; 4.3.3 Example 3; 4.4 Conclusion; References; 5 Fractional Optimal Control of Diffusive Transport Acting on a Spherical Region; 5.1 Introduction; 5.2 Preliminaries; 5.3 Formulation of Axis-Symmetric FOCP; 5.3.1 Half Axis-Symmetric Case; 5.3.2 Complete Axis-Symmetric Case; 5.4 Numerical Results; 5.5 Conclusions; References
  • 6 Integral-Balance Methods for the Fractional Diffusion Equation Described by the Caputo-Generalized Fractional Derivative6.1 Introduction; 6.2 Fractional Calculus News; 6.3 Basics Calculus for the Integral-Balance Methods; 6.4 Integral-Balance Methods; 6.4.1 Approximation with the HBIM; 6.4.2 Approximation with DIM; 6.5 Approximate Solutions of the Generalized Fractional Diffusion Equations; 6.5.1 Quadratic Profile; 6.5.2 Cubic Profile; 6.6 Myers and Mitchell Approach for Exponent n; 6.6.1 Residual Function; 6.6.2 At Boundary Conditions; 6.6.3 Outsides of Boundary Conditions
  • 6.7 ConclusionReferences; 7 A Hybrid Formulation for Fractional Model of Toda Lattice Equations; 7.1 Introduction; 7.2 Basic Idea of HATM with Adomian's Polynomials; 7.3 Application to the Toda Lattice Equations; 7.4 Numerical Result and Discussion; 7.5 Concluding Remarks; Acknowledgements; References; 8 Fractional Model of a Hybrid Nanofluid; 8.1 Introduction; 8.2 Problem's Description; 8.3 Generalization of Local Model; 8.4 Solution of the Problem; 8.4.1 Solutions of the Energy Equation; 8.4.2 Solution of Momentum Equation; 8.5 Results and Discussion; 8.6 Concluding Remarks; Acknowledgment