rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: General fractional derivatives
    sub title: theory, methods and applications
  name:
    name part: Yang, Xiao-Jun
    name part: (Mathematician)
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    date issued: 2019
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource
  abstract: General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.
  table of contents: Cover; Half Title; Title Page; Copyright Page; Dedication; Contents; Preface; Author; 1. Introduction; 1.1 History of fractional calculus; 1.1.1 The contribution for fractional calculus and applications; 1.1.2 The contribution for generalized fractional calculus and applications; 1.2 History of special functions; 1.3 Special functions with respect to another function; 2. Fractional Derivatives of Constant Order and Applications; 2.1 Fractional derivatives within power-law kernel; 2.2 Riemann-Liouville fractional calculus; 2.2.1 Riemann-Liouville fractional integrals
  table of contents: 2.2.2 Riemann-Liouville fractional derivatives2.2.3 Riemann-Liouville fractional derivatives of a purely imaginary order; 2.3 Liouville-Sonine-Caputo fractional derivatives; 2.3.1 Motivations; 2.3.2 Liouville-Sonine-Caputo fractional derivatives; 2.4 Liouville-Grüunwald-Letnikov fractional derivatives; 2.4.1 Motivations; 2.4.2 Liouville-Grüunwald-Letnikov fractional derivatives; 2.4.3 Kilbas-Srivastava-Trujillo fractional derivatives; 2.5 Tarasov type fractional derivatives; 2.5.1 Tarasov type fractional derivatives; 2.5.2 Extended Tarasov type fractional derivatives
  table of contents: 2.6 Riesz fractional calculus2.7 Feller fractional calculus; 2.8 Richard fractional calculus; 2.9 Erdélyi-Kober type fractional calculus; 2.9.1 Erdélyi-Kober type operators of fractional integration and fractional derivative; 2.9.2 Fractional integrals and fractional derivatives of the Erdélyi-Kober-Riesz, Erdélyi-Kober-Feller and Erdélyi-Kober-Rich; 2.10 Katugampola fractional calculus; 2.10.1 Katugampola fractional integrals and Katugampola fractional derivatives; 2.10.2 Katugampola type fractional integrals and Katugampola type fractional derivatives involving the exponential function
  table of contents: 2.11 Hadamard fractional calculus2.11.1 Hadamard fractional integrals and fractional derivatives; 2.11.2 Hadamard type fractional integrals and fractional derivatives; 2.12 Marchaud fractional derivatives; 2.13 Tempered fractional calculus; 2.13.1 Motivations; 2.13.2 Tempered fractional derivatives; 2.13.3 Tempered fractional derivatives with respect to another function; 2.13.4 Tempered fractional derivatives of a purely imaginary order; 2.13.5 Tempered fractional integrals; 2.13.6 Tempered fractional integrals of a purely imaginary order
  table of contents: 2.13.7 Tempered fractional derivatives in the sense of Liouville-Sonine and Liouville-Sonine-Caputo types2.13.8 Tempered fractional derivatives involving power-sine and power-cosine functions; 2.13.9 Tempered fractional calculus involving power-Kohlrausch-Williams-Watts function; 2.13.9.1 Tempered fractional derivative in the Liouville-SonineCaputo type involving the kernel of the power-Kohlrausch-Williams-Watts function; 2.13.9.2 Tempered fractional integral involving the kernel of the power-Kohlrausch-Williams-Watts function; 2.13.10 Sabzikar-Meerschaert-Chen tempered fractional calculus
  note: Xiao-Jun Yang.
  note: "A Chapman & Hall book."
  note: Includes bibliographical references and index.
  subject:
    topic: Fractional calculus
  subject:
    topic: Calculus
  subject:
    topic: Dérivées fractionnaires
  subject:
    topic: Calcul infinitésimal
  subject:
    topic: calculus
  subject:
    topic: MATHEMATICS
    topic: General
  subject:
    topic: MATHEMATICS
    topic: Applied
  subject:
    topic: MATHEMATICS
    topic: Arithmetic
  subject:
    topic: Calculus
  subject:
    topic: Fractional calculus
  classification: QA314
  classification: 515/.83
  related item:
    title info:
      title: General fractional derivatives
    origin info:
      publisher: Boca Raton : CRC Press, Taylor & Francis Group, 2019.
    identifier: (DLC) 2019011932
  identifier: 9780429284083
  identifier: 042928408X
  identifier: 9780429811524
  identifier: 0429811527
  identifier: 9780429811531
  identifier: 0429811535
  identifier: 9780429811517
  identifier: 0429811519
  identifier: 9781138336162
  identifier: 1138336165
  identifier: 2020694214
  identifier: 9780429284083 Taylor & Francis
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: DLC
    record creation date: 190314
    record change date: 20241111204832.6
    record identifier: in00005528934
    language of cataloging:
      language term: eng