Handbook of Fractional Calculus with Applications.

Handbook of Fractional Calculus with Applications. / Volume 2, : Fractional Differential Equations / / ed. by Anatoly Kochubei, Yuri Luchko.

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differentia...

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Superior document:Title is part of eBook package: De Gruyter DG Plus eBook-Package 2019
MitwirkendeR:
Aleroev, Temirkhan,
Aleroeva, Hedi,
Atanacković, Teodor M.,
Diethelm, Kai,
Edelman, Mark,
Gazizov, Rafail K.,
Jleli, Mohamed,
Kasatkin, Alexey A.,
Kemppainen, Jukka,
Kirane, Mokhtar,
Knopova, Victoria P.,
Kochubei, Anatoly N.,
Konjik, Sanja,
Kulik, Alexei M.,
Li, Zhiyuan,
Liu, Yikan,
Lizama, Carlos,
Luchko, Yuri,
Lukashchuk, Stanislav Yu.,
Pilipović, Stevan,
Samet, Bessem,
Stinga, Pablo Raúl,
Umarov, Sabir,
Yamamoto, Masahiro,
Zacher, Rico,
HerausgeberIn:
Kochubei, Anatoly,
Luchko, Yuri,
Place / Publishing House:Berlin ;, Boston : : De Gruyter, , [2019]
©2019
Year of Publication:2019
Language:English
Series:De Gruyter Reference ; Volume 2
Online Access:
Physical Description:1 online resource (VIII, 519 p.)
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Table of Contents:
  • Frontmatter
  • Preface
  • Contents
  • General theory of Caputo-type fractional differential equations
  • Problems of Sturm–Liouville type for differential equations with fractional derivatives
  • Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps
  • Symmetries and group invariant solutions of fractional ordinary differential equations
  • Operational method for fractional ordinary differential equations
  • Lyapunov-type inequalities for fractional boundary value problems
  • Fractional-parabolic equations and systems. Cauchy problem
  • Time fractional diffusion equations: solution concepts, regularity, and long-time behavior
  • Layer potentials for the time-fractional diffusion equation
  • Fractional-hyperbolic equations and systems. Cauchy problem
  • Equations with general fractional time derivatives–Cauchy problem
  • User’s guide to the fractional Laplacian and the method of semigroups
  • Parametrix methods for equations with fractional Laplacians
  • Maximum principle for the time-fractional PDEs
  • Wave equation involving fractional derivatives of real and complex fractional order
  • Symmetries, conservation laws and group invariant solutions of fractional PDEs
  • Fractional Duhamel principle
  • Inverse problems of determining sources of the fractional partial differential equations
  • Inverse problems of determining parameters of the fractional partial differential equations
  • Inverse problems of determining coefficients of the fractional partial differential equations
  • Abstract linear fractional evolution equations
  • Abstract nonlinear fractional evolution equations
  • Index

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