Methods of Mathematical Modelling Fractional Differential Equations. [electronic resource] :
- Milton : CRC Press LLC, 2019.
- 1 online resource (255 p.).
- Mathematics and Its Applications .
Description based upon print version of record.
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
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 physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications
9781000596786 1000596788 9780429274114 0429274114 9781000606485 1000606481 9781000601633 1000601633
TECHNOLOGY / Engineering / Industrial
TECHNOLOGY / Manufacturing
MATHEMATICS / Applied
Mathematical models.
Fractional differential equations.
TA342
515.35
Description based upon print version of record.
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
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 physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications
9781000596786 1000596788 9780429274114 0429274114 9781000606485 1000606481 9781000601633 1000601633
TECHNOLOGY / Engineering / Industrial
TECHNOLOGY / Manufacturing
MATHEMATICS / Applied
Mathematical models.
Fractional differential equations.
TA342
515.35