Handbook of Fractional Calculus with Applications: Fractional Differential Equations (De Gruyter Reference)

Description

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. Cover Handbook of Fractional Calculus with Applications, Volume 2: Fractional Differential Equations © 2019 Preface Contents 1 General theory of Caputo-type fractional differential equations 2 Problems of Sturm–Liouville type for differential equations with fractional derivatives 3 Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps 4 Symmetries and group invariant solutions of fractional ordinary differential equations 5 Operational method for fractional ordinary differential equations 6 Lyapunov-type inequalities for fractional boundary value problems 7 Fractional-parabolic equations and systems. Cauchy problem 8 Time fractional diffusion equations: solution concepts, regularity, and long-time behavior 9 Layer potentials for the time-fractional diffusion equation 10 Fractional-hyperbolic equations and systems. Cauchy problem 11 Equations with general fractional time derivatives—Cauchy problem 12 User’s guide to the fractional Laplacian and the method of semigroups 13 Parametrix methods for equations with fractional Laplacians 14 Maximum principle for the time-fractional PDEs 15 Wave equation involving fractional derivatives of real and complex fractional order 16 Symmetries, conservation laws and group invariant solutions of fractional PDEs 17 Fractional Duhamel principle 18 Inverse problems of determining sources of the fractional partial differential equations 19 Inverse problems of determining parameters of the fractional partial differential equations 20 Inverse problems of determining coefficients of the fractional partial differential equations 21 Abstract linear fractional evolution equations 22 Abstract nonlinear fractional evolution equations Index