Fractional Differential Equations 1st Edition by Anatoly Kochubei, Yuri Luchko ISBN 3110571056 9783110571059

Here’s a more organized presentation of the topics you provided, grouped logically by their thematic content:

1. General Theory and Methods for Fractional Differential Equations

• General theory of Caputo-type fractional differential equations
• Operational method for fractional ordinary differential equations
• User’s guide to the fractional Laplacian and the method of semigroups
• Parametrix methods for equations with fractional Laplacians
• Abstract linear fractional evolution equations
• Abstract nonlinear fractional evolution equations

2. Boundary Value Problems and Inequalities

• Lyapunov-type inequalities for fractional boundary value problems
• Problems of Sturm–Liouville type for differential equations with fractional derivatives
• 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

3. Fractional Partial Differential Equations (PDEs) and Systems

• Fractional-parabolic equations and systems. Cauchy problem
• Fractional-hyperbolic equations and systems. Cauchy problem
• Equations with general fractional time derivatives—Cauchy problem
• Time fractional diffusion equations: solution concepts, regularity, and long-time behavior
• Layer potentials for the time-fractional diffusion equation
• Maximum principle for the time-fractional PDEs
• Wave equation involving fractional derivatives of real and complex fractional order

4. Symmetries, Group Invariants, and Conservation Laws

• Symmetries and group invariant solutions of fractional ordinary differential equations
• Symmetries, conservation laws, and group invariant solutions of fractional PDEs

5. Fractional Maps and Power-Law Memory

• Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps

6. Principles and Advanced Topics

• Fractional Duhamel principle
• Inverse problems related to fractional PDEs