04261cam a2200505Ii 4500 ocn922324031 OCoLC 20190328114812.0 m o d cr cnu|||unuuu 150928t20152016enk ob 000 0 eng d N$T eng rda pn N$T OPELS YDXCP N$T IDEBK CDX OCLCF EBLCP DEBSZ OCLCQ WRM U3W D6H OCLCQ ZCU 929521692 9780128038253 (electronic bk.) 012803825X (electronic bk.) 9780081006443 (OCoLC)922324031 (OCoLC)929521692 QA325 MAT 005000 bisacsh MAT 034000 bisacsh 515/.33 23 Atangana, Abdon, author. Derivative with a new parameter : theory, methods and applications / [electronic resource] Abdon Atangana. London, UK : Academic Press is an imprint of Elsevier, 2015. �2016 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references. Online resource; title from PDF title page (ScienceDirect, viewed September 29, 2015). Title page; Table of Contents; Copyright; 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 parameter2.5 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 method4.6 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. Annotation This text 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. Derivatives (Mathematics) Differential calculus. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Derivatives (Mathematics) fast (OCoLC)fst01893449 Differential calculus. fast (OCoLC)fst00893441 Electronic books. Print version: Atangana, Abdon. Derivative with a New Parameter : Theory, Methods and Applications. : Elsevier Science, �2015 9780081006443 ScienceDirect http://www.sciencedirect.com/science/book/9780081006443 247173 247173