Derivative with a new parameter : theory, methods and applications / Abdon Atangana.

Format:

Book

Author/Creator:

Atangana, Abdon, author.

Language:

English

Subjects (All):

Derivatives (Mathematics).

Differential calculus.

Physical Description:

1 online resource (0 p.)

Edition:

1st ed.

Place of Publication:

Amsterdam, [Netherlands] : Academic Press, 2016.

Language Note:

English

Summary:

Derivative with a New Parameter: Theory, Methods and Applications discusses the first application of the local derivative that was done by Newton for general physics, and later for other areas of the sciences.The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes on to introduce the new parameters for the local derivative, including its definition and properties. Additional topics define beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, including their properties, and then go on to describe the method for partial differential with the beta derivatives.Subsequent sections give examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases. The book gives an introduction to the newly-established local derivative with new parameters, along with their integral transforms and applications, also including great examples on how it can be used in epidemiology and groundwater studies.- Introduce the new parameters for the local derivative, including its definition and properties- Provides examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseases- Includes definitions of beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, their properties, and methods for partial differential using beta derivatives- Explains how the new parameter can be used in multiple methods

Contents:

Front Cover

Derivative with a New Parameter: Theory, Methods and Applications

Copyright

Dedication

Contents

Preface

Acknowledgments

Chapter 1: History of derivatives from Newton to Caputo

1.1 Introduction

1.2 Definition of local and fractional derivative

1.3 Definitions and properties of their anti-derivatives

1.3.1 Anti-derivative with integer order

1.3.2 Anti-derivative with non-integer order

1.3.3 Integral of variable order

1.4 Limitations and strength of local and fractional derivatives

1.4.1 Advantages of fractional derivatives

1.4.2 Disadvantages of fractional derivatives

1.5 Classification of fractional derivatives

1.5.1 Criteria of fractional derivatives

Chapter 2: Local derivative with new parameter

2.1 Motivation

2.2 Definition and anti-derivative

2.3 Properties of local derivative with new parameter

2.4 Definition of partial derivative with new parameter

2.5 Properties of partial beta-derivatives

Chapter 3: Novel integrals transform

3.1 Definition of some integral transform operators

3.2 Definition and properties of the beta-Laplace transform

3.2.1 Properties of the beta-Laplace transform

3.3 Definition and properties of the beta-Sumudu transform

3.3.1 Properties of beta-Sumudu transform

3.4 Definition and properties of beta-Fourier transform

3.4.1 Properties of the beta-Fourier transform

Chapter 4: Method for partial differential equations with beta-derivative

4.1 Introduction

4.2 Homotopy decomposition method

4.3 Variational iteration method

4.3.1 Methodology and stability analysis

4.4 Sumudu decomposition method

4.5 Laplace decomposition method

4.6 Extension of match asymptotic method to fractional boundary layers problems

4.6.1 Methodology

4.7 Numerical method.

4.8 Generalized stationarity with a new parameter

4.8.1 Generalized time evolution

4.8.2 Basic settings for time evolutions hilfer

4.8.3 Diffusion using derivative with a new parameter

Chapter 5: Applications of local derivative with new parameter

5.1 Introduction

5.2 Model of groundwater flow within the confined aquifer

5.2.1 Derivation of analytical solution

5.3 Steady-state solutions of the flow in a confined and unconfined aquifer

5.3.1 Steady-state solution of the flow in a confined aquifer

5.3.2 Steady-state solution of the flow in an unconfined aquifer

5.4 Model of groundwater flow equation within a leaky aquifer

5.4.1 Special solution via iteration method

5.4.2 Stability and convergence analysis

5.4.3 Uniqueness analysis of the special solution

5.4.4 Numerical simulation

5.5 Model of Lassa fever or Lassa hemorrhagic fever

5.5.1 Mathematical model of Lassa using the beta-derivative

5.5.2 Analysis of equilibrium points

5.5.3 Application to model of Lassa fever with beta-derivative

5.5.4 Special analytical solution via an iterative method with Atangana's transform

5.5.5 Stability and unicity analysis for the iteration method

5.6 Model of Ebola hemorrhagic fever

5.6.1 Signs and symptoms

5.6.2 Transmission

5.6.3 Host of Ebolavirus

5.6.4 Pathophysiology

5.6.5 Prevention of viral hemorrhagic fever

5.6.6 Mathematical model of EHF via beta-derivative

5.6.7 Control of the disease via mathematical analysis

5.6.8 Analysis and validation

5.6.9 Derivation of the solution via the iterative method

5.6.10 Numerical solutions

Bibliography

Back cover.

Notes:

Description based upon print version of record

Includes bibliographical references.

Description based on online resource; title from PDF title page (ebrary, viewed December 4, 2015).

ISBN:

9780128038253

012803825X

9780081006443

0081006446

OCLC:

932328744