The first application of the local derivative was done by Newton for general physics and later on in other areas of sciences. However the local derivative was not able to explain some complex physical problems. Therefore fractional calculus and fractional order models were studied to try and solve these problems. There were further problems with fractional derivatives such as they do not obey some classical properties of calculus. Therefore a new derivative was introduced and called beta-derivative. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes onto introduce the new parameter for the local derivative, including the definition and properties. Another part of the book defines beta-Laplace transforms, beta-Sumudu transforms and beta-Fourier transforms and gives the properties of them. It then goes onto describe the method for partial differential with the beta derivative. It then ends with giving examples of how local derivative with a new parameter can be used to model different applications, such as groundwater flow and different diseases. Derivative with a new parameter gives an introduction to the newly-established local derivative with new parameters together with theirs integral transforms and their applications. It gives great examples of how it can be used in epidemiology and groundwater studies. Introduces the new parameter of the local derivativeExplains how the new parameter can be used in multiple methodsDiscusses different applications, such as modelling of different INDICE: Chapter 1. History of derivatives from Newton to Caputo1.1: 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 derivativesChapter 2: Local derivative with new parameter2.1: Definition and anti-derivative2.2: Properties of local derivative with new parameter2.3: Definition Partial derivative with new parameter 2.4: Properties of partial derivatives with new parametersChapter 3: Novel integral transform 3.1: Definition and properties of beta-Laplace transform3.2: Definition and properties of beta-Sumudu transform3.3: Definition and properties of beta-Fourier transformChapter 4: Method for partial differential with beta derivative4.1: Homotopy decomposition method4.2: Variational iteration method4.3: Sumudu decomposition method4.4: Laplace decomposition method 4.5: Numerical method Chapter 5: Applications of local derivative with new parameter5.1: Model of groundwater flow within the confined aquifer5.2: Model of groundwater flow equation within a leaky aquifer5.3: Model of Lassa fever or Lassa hemorrhagic fever 5.4: Model of Ebola hemorrhagic fever References
- ISBN: 978-0-08-100644-3
- Editorial: Academic Press
- Encuadernacion: Rústica
- Páginas: 100
- Fecha Publicación: 01/10/2015
- Nº Volúmenes: 1
- Idioma: Inglés