Methods of Mathematical Modelling

Fractional Differential Equations

Harendra Singh, Devendra Kumar, Dumitru Baleanu

• Publisher: CRC Press
• Year: 2019
• eBook ISBN: 9781000606485
• Edition: 1
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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

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• Presents several recent developments in the theory and applications of fractional calculus

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• Includes chapters on different analytical and numerical methods dedicated to several mathematical equations

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• Develops methods for the mathematical models which are governed by fractional differential equations

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• Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering

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• Discusses real-world problems, theory, and applications

1

Mathematical Analysis and Simulation of Chaotic Tritrophic Ecosystem Using Fractional Derivatives with Mittag-Leffler Kernel

Kolade M. Owolabi

University of the Free State
Federal University of Technology

Berat Karaagac

Adyaman University

CONTENTS

• 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
• References

1.1 Introduction

In the past few decades, population systems consisting of one or two species have attracted the attention of scientists and other scholars [2, 10, 15, 16 and 17, 25, 28]. It was observed that only a few handful of research findings report...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Table of Contents
• Perface
• Editors
• Contributors
• 1 Mathematical Analysis and Simulation of Chaotic Tritrophic Ecosystem Using Fractional Derivatives with Mittag-Leffler Kernel
• 2 Solutions for Fractional Diffusion Equations with Reactive Boundary Conditions
• 3 An Efficient Computational Method for Non-Linear Fractional Lienard Equation Arising in Oscillating Circuits
• 4 A New Approximation Scheme for Solving Ordinary Differential Equation with Gomez–Atangana–Caputo Fractional Derivative
• 5 Fractional Optimal Control of Diffusive Transport Acting on a Spherical Region
• 6 Integral-Balance Methods for the Fractional Diffusion Equation Described by the Caputo-Generalized Fractional Derivative
• 7 A Hybrid Formulation for Fractional Model of Toda Lattice Equations
• 8 Fractional Model of a Hybrid Nanofluid
• 9 Collation Analysis of Fractional Moisture Content Based Model in Unsaturated Zone Using q-homotopy Analysis Method
• 10 Numerical Analysis of a Chaotic Model with Fractional Differential Operators: From Caputo to Atangana–Baleanu
• 11 A New Numerical Method for a Fractional Model of Non-Linear Zakharov–Kuznetsov Equations via Sumudu Transform
• 12 Chirped Solitons with Fractional Temporal Evolution in Optical Metamaterials
• 13 Controllability on Non-dense Delay Fractional Differential System with Non-Local Conditions
• Index