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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
Scientists and engineers in the fields of mathematics, physics, chemistry and engineering
- 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
- 1.4 Limitations and strength of local and fractional derivatives
- 1.5 Classification 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
- 3.3 Definition and properties of the beta-Sumudu transform
- 3.4 Definition and properties of 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
- 4.4 Sumudu decomposition method
- 4.5 Laplace decomposition method
- 4.6 Extension of match asymptotic method to fractional boundary layers problems
- 4.7 Numerical method
- 4.8 Generalized stationarity 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
- 5.3 Steady-state solutions of the flow in a confined and unconfined aquifer
- 5.4 Model of groundwater flow equation within a leaky aquifer
- 5.5 Model of Lassa fever or Lassa hemorrhagic fever
- 5.6 Model of Ebola hemorrhagic fever
- No. of pages:
- © Academic Press 2016
- 10th September 2015
- Academic Press
- Paperback ISBN:
- eBook ISBN:
Abdon Atangana’s serves as Professor at the University of Free State in Bloemfontein, South Africa. He specializes in applied mathematics, groundwater modeling, fractional calculus and their applications, methods for partial differential equations, methods for ordinary differential equations, iterations methods, asymptotic methods, perturbations methods, and numerical method for fractional differential equations, uncertainties analysis. He has participated in 18 international conferences, organized 6 special sections and symposium in international conference in Europe, Africa, Asia and USA, and has been invited as plenary speaker in 8 international conferences. He serves as editor for an international journal of applied mathematics and is the editor-in-chief for two international journals. He has authored more than 145 research papers in international accredited journals of mathematics and applied mathematics. His previous book, “Derivative with a New Parameter: Theory, Methods and Applications”, was published with Elsevier Sep-15, 2015.
University of the Free State, Bloemfontein, South Africa
"To define a new integral transform, in addition to the definition one must provide an inversion theorem, existence and uniqueness theorems." --Zentralblatt MATH
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