Methods of Mathematical Modelling: Fractional Differential Equations


Download Methods of Mathematical Modelling: Fractional Differential Equations written by Harendra Singh, Devendra Kumar, Dumitru Baleanu in PDF format. This book is under the category Mathematics and bearing the isbn/isbn13 number 0367220083; 0429274114; 0367776553; 1000606481/9780367220082/ 9780429274114/ 9780367776558/ 9781000606485. You may reffer the table below for additional details of the book.


Methods of Mathematical Modelling: Fractional Differential Equations; (PDF) options unique analysis articles on the topic of mathematical modeling and fractional differential equations. The contributions; written by distinguished researchers within the discipline; comprised of chapters on classical and trendy dynamical programs modeled by fractional differential equations in physics; sign processing; fluid mechanics; engineering; and bioengineering; programs engineering; manufacturing; and challenge administration.

The ebook provides idea and sensible purposes for the solutions of actual-life issues and shall be of curiosity to graduate-stage college students; researchers; educators; and scientists fascinated by mathematical modeling and its various purposes.


  • Presents quite a few current developments within the idea and purposes of fractional calculus
  • Constructs strategies for the mathematical fashions that are dominated by fractional differential equations
  • Includes chapters on totally different numerical and analytical strategies devoted to a number of mathematical equations
  • Provides strategies for fashions in numerous fields like physics; sign processing; engineering; fluid mechanics; and bioengineering

Discusses actual-world issues; idea; and purposes

NOTE: The product solely contains the ebook Methods of Mathematical Modelling: Fractional Differential Equations in PDF. No access codes are included.

Additional information


Harendra Singh, Devendra Kumar, Dumitru Baleanu


CRC Press; 1st edition










0367220083; 0429274114; 0367776553; 1000606481


9780367220082/ 9780429274114/ 9780367776558/ 9781000606485

Table of contents

Table of contents :
Half Title
Series Page
Title Page
Copyright Page
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
2 Solutions for Fractional Diffusion Equations
with Reactive Boundary Conditions
2.1 Introduction
2.2 The Problem: Diffusion and Kinetics
2.3 Discussion and Conclusions
3 An Efficient Computational Method for
Non-Linear Fractional Lienard Equation
Arising in Oscillating Circuits
3.1 Introduction
3.2 Preliminaries
3.3 Method of Solution
3.4 Numerical Experiments and Discussion
3.5 Conclusions
3.6 Application
4 A New Approximation Scheme for Solving
Ordinary Differential Equation with
Gomez-Atangana-Caputo Fractional
4.1 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
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
6 Integral-Balance Methods for the
Fractional Diffusion Equation
Described by the Caputo-Generalized
Fractional Derivative
6.1 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 Conclusion
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
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
9 Collation Analysis of Fractional Moisture
Content Based Model in Unsaturated Zone
Using q-homotopy Analysis Method
9.1 Introduction
9.2 Mathematical Preliminaries
9.3 Fractional Moisture Content Based Model
9.4 Applications
9.5 Numerical Simulation
9.6 Conclusion
10 Numerical Analysis of a Chaotic Model
with Fractional Differential Operators:
From Caputo to Atangana-Baleanu
10.1 Introduction
10.2 Basic Definitions of Fractional Calculus
10.3 New Numerical Scheme with Atangana-Baleanu Fractional Derivative
10.4 Numerical Scheme with Caputo Fractional Derivative
10.5 Numerical Scheme for Caputo-Fabrizio Fractional Derivative
10.6 Existence and Uniqueness Condition for Atangana-Baleanu Fractional Derivative
10.7 Existence and Uniqueness Condition for Caputo Fractional Derivative
10.8 Existence and Uniqueness Condition for Caputo-Fabrizio Fractional Derivative
10.9 Conclusion
11 A New Numerical Method for a Fractional
Model of Non-Linear Zakharov-Kuznetsov
Equations via Sumudu Transform
11.1 Introduction
11.2 Preliminaries
11.3 Adomian Decomposition Sumudu Transform Method
11.4 Error Analysis of the Proposed Technique
11.5 Test Examples
11.6 Conclusion
12 Chirped Solitons with Fractional Temporal
Evolution in Optical Metamaterials
12.1 Introduction
12.2 Model Description
12.2.1 The Modified Riemann-Liouville Derivative and Bessel’s Equation
12.2.2 Solutions of Schrödinger Equation
12.2.3 Soliton Solution
12.3 Conclusion
13 Controllability on Non-dense Delay
Fractional Differential System with
Non-Local Conditions
13.1 Introduction
13.2 Preparatory Results
13.3 Results on Controllability
13.4 Conclusion

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