Derivative with a New Parameter

Derivative with a New Parameter

Theory, Methods and Applications

1st Edition - September 10, 2015

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  • Author: Abdon Atangana
  • eBook ISBN: 9780128038253
  • Paperback ISBN: 9780081006443

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Description

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.

Key Features

  • 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

Readership

Scientists and engineers in the fields of mathematics, physics, chemistry and engineering

Table of Contents

    • Dedication
    • Preface
    • Acknowledgments
    • Chapter 1: History of derivatives from Newton to Caputo
      • Abstract
      • 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
      • Abstract
      • 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
      • Abstract
      • 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
      • Abstract
      • 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
      • Abstract
      • 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
    • Bibliography

Product details

  • No. of pages: 170
  • Language: English
  • Copyright: © Academic Press 2015
  • Published: September 10, 2015
  • Imprint: Academic Press
  • eBook ISBN: 9780128038253
  • Paperback ISBN: 9780081006443

About the Author

Abdon Atangana

Dr. Atangana is Academic Head of Department and Professor of Applied Mathematics at the University of the Free State, Bloemfontein, Republic of South Africa. He obtained his honours and master’s degrees from the Department of Applied Mathematics at the UFS with distinction. He obtained his PhD in applied mathematics from the Institute for Groundwater Studies. He serves as an editor for 20 international journals and lead guest editor in 10 journals and is also a reviewer of more than 200 international accredited journals. His research interests are methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modelling. Prof Atangana is the founder of fractional calculus with non-local and non-singular kernels popular in applied mathematics today. Since 2013, he has published in 250 international accredited journals of applied mathematics, applied physics, geo-hydrology and biomathematics. He is also the single author of two books in Academic Press Elsevier and a co-author of a book published in springer and author of more than 20 chapters in books. He has graduated 7 PhD and 20 masters students, and 6 postdoc fellows.

Affiliations and Expertise

Academic Head of Department and Professor of Applied Mathematics, University of the Free State, Bloemfontein, South Africa

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