Handbook of Fractional Calculus with Applications. Volume 2, Fractional Differential Equations

Frontmatter --
Preface --
Contents --
General theory of Caputo-type fractional differential equations / Diethelm, Kai --
Problems of Sturm–Liouville type for differential equations with fractional derivatives / Aleroev, Temirkhan / Aleroeva, Hedi --
Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps / Edelman, Mark --
Symmetries and group invariant solutions of fractional ordinary differential equations / Gazizov, Rafail K. / Kasatkin, Alexey A. / Lukashchuk, Stanislav Yu. --
Operational method for fractional ordinary differential equations / Luchko, Yuri --
Lyapunov-type inequalities for fractional boundary value problems / Jleli, Mohamed / Kirane, Mokhtar / Samet, Bessem --
Fractional-parabolic equations and systems. Cauchy problem / Kochubei, Anatoly N. --
Time fractional diffusion equations: solution concepts, regularity, and long-time behavior / Zacher, Rico --
Layer potentials for the time-fractional diffusion equation / Kemppainen, Jukka --
Fractional-hyperbolic equations and systems. Cauchy problem / Kochubei, Anatoly N. --
Equations with general fractional time derivatives–Cauchy problem / Kochubei, Anatoly N. --
User’s guide to the fractional Laplacian and the method of semigroups / Stinga, Pablo Raúl --
Parametrix methods for equations with fractional Laplacians / Knopova, Victoria P. / Kochubei, Anatoly N. / Kulik, Alexei M. --
Maximum principle for the time-fractional PDEs / Luchko, Yuri / Yamamoto, Masahiro --
Wave equation involving fractional derivatives of real and complex fractional order / Atanacković, Teodor M. / Konjik, Sanja / Pilipović, Stevan --
Symmetries, conservation laws and group invariant solutions of fractional PDEs / Gazizov, Rafail K. / Kasatkin, Alexey A. / Lukashchuk, Stanislav Yu. --
Fractional Duhamel principle / Umarov, Sabir --
Inverse problems of determining sources of the fractional partial differential equations / Liu, Yikan / Li, Zhiyuan / Yamamoto, Masahiro --
Inverse problems of determining parameters of the fractional partial differential equations / Li, Zhiyuan / Liu, Yikan / Yamamoto, Masahiro --
Inverse problems of determining coefficients of the fractional partial differential equations / Li, Zhiyuan / Yamamoto, Masahiro --
Abstract linear fractional evolution equations / Lizama, Carlos --
Abstract nonlinear fractional evolution equations / Lizama, Carlos --
Index