General fractional derivatives with applications in viscoelasticity /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Yang, Xiao-Jun (Mathematician)
Otros Autores: Gao, Feng, Yang, Ju
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London : Academic Press, 2020.
Temas:
Fractional calculus.
Viscoelasticity > Mathematics.
D�eriv�ees fractionnaires.
Visco�elasticit�e > Math�ematiques.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover
  • General Fractional Derivatives With Applications in Viscoelasticity
  • Copyright
  • Contents
  • Preface
  • 1 Special functions
  • 1.1 Euler gamma and beta functions
  • 1.1.1 Euler gamma function
  • 1.1.2 Euler beta function
  • 1.2 Laplace transform and properties
  • 1.3 Mittag-Lef er function
  • 1.4 Miller-Ross function
  • 1.5 Rabotnov function
  • 1.6 One-parameter Lorenzo-Hartley function
  • 1.7 Prabhakar function
  • 1.8 Wiman function
  • 1.9 The two-parameter Lorenzo-Hartley function
  • 1.10 Two-parameter Goren o-Mainardi function
  • 1.11 Euler-type gamma and beta functions with respect to another function
  • 1.12 Mittag-Lef er-type function with respect to another function
  • 1.13 Miller-Ross-type function with respect to function
  • 1.14 Rabotnov-type function with respect to another function
  • 1.15 Lorenzo-Hartley-type function with respect to another function
  • 1.16 Prabhakar-type function with respect to another function
  • 1.17 Wiman-type function with respect to another function
  • 1.18 Two-parameter Lorenzo-Hartley function with respect to another function
  • 1.19 Goren o-Mainardi-type function with respect to another function
  • 2 Fractional derivatives with singular kernels
  • 2.1 The space of the functions
  • 2.1.1 The set of Lebesgue measurable functions
  • 2.1.2 The weighted space with the power weight
  • 2.1.3 The space of absolutely continuous functions
  • 2.1.4 The Kolmogorov-Fomin condition
  • 2.1.5 The Samko-Kilbas-Marichev condition
  • 2.2 Riemann-Liouville fractional calculus
  • 2.2.1 Riemann-Liouville fractional integrals
  • 2.2.2 Riemann-Liouville fractional derivatives
  • 2.3 Osler fractional calculus
  • 2.4 Liouville-Weyl fractional calculus
  • 2.4.1 Liouville-Weyl fractional integrals
  • 2.4.2 Liouville-Weyl fractional derivatives
  • 2.5 Samko-Kilbas-Marichev fractional calculus
  • 2.5.1 Samko-Kilbas-Marichev fractional integrals
  • 2.5.2 Samko-Kilbas-Marichev fractional derivatives
  • 2.6 Liouville-Sonine-Caputo fractional derivatives
  • 2.6.1 History of Liouville-Sonine-Caputo fractional derivatives
  • 2.7 Liouville fractional derivatives
  • 2.8 Almeida fractional derivatives with respect to another function
  • 2.9 Liouville-type fractional derivative with respect to another function
  • 2.10 Liouville-Gr�unwald-Letnikov fractional derivatives
  • 2.10.1 History of the Liouville-Gr�unwald-Letnikov fractional derivatives
  • 2.10.2 Concepts of Liouville-Gr�unwald-Letnikov fractional derivatives
  • 2.10.3 Liouville-Gr�unwald-Letnikov fractional derivatives on a bounded domain
  • 2.11 Kilbas-Srivastava-Trujillo fractional difference derivatives
  • 2.12 Riesz fractional calculus
  • 2.12.1 Riesz fractional calculus
  • 2.12.2 Riesz-type fractional calculus
  • 2.12.3 Liouville-Sonine-Caputo-Riesz-type fractional derivatives
  • 2.13 Feller fractional calculus

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