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

• 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
• Physical Description: 1 online resource (VIII, 519 p.)

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 differential equations of fractional order, inverse problems, and evolution equations.

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