Derivative with a New Parameter: Theory, Methods and Applications

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 propertiesProvides examples on how local derivatives with a new parameter can be used to model different applications, such as groundwater flow and different diseasesIncludes definitions of beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, their properties, and methods for partial differential using beta derivativesExplains how the new parameter can be used in multiple methods

Chapter 1. History of derivatives from Newton to Caputo
1.1: Introduction of calculus
1.2: Definition of local and fractional derivative
1.3: Definitions and Properties of their anti-derivatives (Integral)
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: Definition and anti-derivative
2.2: Properties of local derivative with new parameter
2.3: Definition Partial derivative with new parameter
2.4: Properties of partial derivatives with new parameters
Chapter 3: Novel integral transform
3.1: Definition and properties of beta-Laplace transform
3.2: Definition and properties of beta-Sumudu transform
3.3: Definition and properties of beta-Fourier transform
Chapter 4: Method for partial differential with beta derivative
4.1:  Homotopy  decomposition method
4.2: Variational iteration method
4.3:  Sumudu decomposition method
4.4: Laplace decomposition method
4.5: Numerical method
Chapter 5:  Applications of local derivative with new parameter
5.1: Model of groundwater flow within the confined aquifer
5.2: Model of groundwater flow equation within a leaky aquifer
5.3: Model of Lassa fever or Lassa hemorrhagic fever
5.4: Model of Ebola hemorrhagic fever
References