Singh H., Kumar D., Baleanu D. (eds.) Methods of Mathematical Modelling: Fractional Differential Equations

Boca Raton: CRC Press, 2019. — 255 p.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.FeaturesPresents 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 applicationsEditorsMathematical Analysis and Simulation of Chaotic Tritrophic Ecosystem Using Fractional Derivatives with Mittag-Leffler KernelMethod of Approximation of Fractional Derivative
Model Equations and Stability Analysis
Fractional Food Chain Dynamics with Holling Type II Functional Response
Multi-Species Ecosystem with a Beddington-DeAngelis Functional Response
Numerical Experiment for Fractional Reaction-Diffusion EcosystemSolutions for Fractional Diffusion Equations with Reactive Boundary ConditionsThe Problem: Diffusion and Kinetics
Discussion and Conclusions
AcknowledgementAn Efficient Computational Method for Non-Linear Fractional Lienard Equation
Arising in Oscillating CircuitsPreliminaries
Method of Solution
Numerical Experiments and Discussion
Conclusions
Application
AppendixA New Approximation Scheme for Solving
Ordinary Differential Equation with Gomez-Atangana-Caputo Fractional
DerivativeA New Numerical Approximation
Error Estimate
Application
Example
Example
ExampleFractional Optimal Control of Diffusive Transport Acting on a Spherical RegionPreliminaries
Formulation of Axis-Symmetric FOCP
Half Axis-Symmetric Case
Complete Axis-Symmetric Case
Numerical Results
ConclusionsIntegral-Balance Methods for the Fractional Diffusion Equation
Described by the Caputo-Generalized
Fractional DerivativeFractional Calculus News
Basics Calculus for the Integral-Balance Methods
Integral-Balance Methods
Approximation with the HBIM
Approximation with DIM
Approximate Solutions of the Generalized Fractional Diffusion Equations
Quadratic Profile
Cubic Profile
Myers and Mitchell Approach for Exponent n
Residual Function
At Boundary Conditions
Outsides of Boundary ConditionsA Hybrid Formulation for Fractional Model of Toda Lattice EquationsBasic Idea of HATM with Adomian's Polynomials
Application to the Toda Lattice Equations
Numerical Result and Discussion
Concluding Remarks
AcknowledgementsFractional Model of a Hybrid NanofluidProblem's Description
Generalization of Local Model
Solution of the Problem
Solutions of the Energy Equation
Solution of Momentum Equation
Results and Discussion
Concluding RemarksCollation Analysis of Fractional Moisture Content Based Model in Unsaturated Zone
Using q-homotopy Analysis MethodMathematical Preliminaries
Fractional Moisture Content Based Model
Applications
Numerical SimulationNumerical Analysis of a Chaotic Model with Fractional Differential Operators:
From Caputo to Atangana-BaleanuBasic Definitions of Fractional Calculus
New Numerical Scheme with Atangana-Baleanu Fractional Derivative
Numerical Scheme with Caputo Fractional Derivative
Numerical Scheme for Caputo-Fabrizio Fractional Derivative
Existence and Uniqueness Condition for Atangana-Baleanu Fractional Derivative
Existence and Uniqueness Condition for Caputo Fractional Derivative
Existence and Uniqueness Condition for Caputo-Fabrizio Fractional DerivativeA New Numerical Method for a Fractional
Model of Non-Linear Zakharov-Kuznetsov
Equations via Sumudu TransformPreliminaries
Adomian Decomposition Sumudu Transform Method
Error Analysis of the Proposed Technique
Test ExamplesChirped Solitons with Fractional Temporal Evolution in Optical MetamaterialsModel Description
The Modified Riemann-Liouville Derivative and Bessel's Equation
Solutions of Schrödinger Equation
Soliton SolutionControllability on Non-dense Delay Fractional Differential System with
Non-Local ConditionsPreparatory Results
Results on Controllability