LEADER 04530nam 2200493 450 001 996466415303316 005 20231110233020.0 010 $a3-030-76043-X 035 $a(CKB)4100000011984431 035 $a(MiAaPQ)EBC6682760 035 $a(Au-PeEL)EBL6682760 035 $a(OCoLC)1261380047 035 $a(PPN)258059540 035 $a(EXLCZ)994100000011984431 100 $a20220411d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFractional differential equations $ean approach via fractional derivatives /$fBangti Jin 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (377 pages) 225 1 $aApplied Mathematical Sciences ;$vv.206 311 $a3-030-76042-1 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- Acronyms -- Part I Preliminaries -- 1 Continuous Time Random Walk -- 1.1 Random Walk on a Lattice -- 1.2 Continuous Time Random Walk -- 1.3 Simulating Continuous Time Random Walk -- 2 Fractional Calculus -- 2.1 Gamma Function -- 2.2 Riemann-Liouville Fractional Integral -- 2.3 Fractional Derivatives -- 2.3.1 Riemann-Liouville fractional derivative -- 2.3.2 Djrbashian-Caputo fractional derivative -- 2.3.3 Gru?nwald-Letnikov fractional derivative -- 3 Mittag-Leffler and Wright Functions -- 3.1 Mittag-Leffler Function -- 3.1.1 Basic analytic properties -- 3.1.2 Mittag-Leffler function E?,1(-x) -- 3.2 Wright Function -- 3.2.1 Basic analytic properties -- 3.2.2 Wright function W?,µ(-x) -- 3.3 Numerical Algorithms -- 3.3.1 Mittag-Leffler function E?,?(z) -- 3.3.2 Wright function W?,µ(x) -- Part II Fractional Ordinary Differential Equations -- 4 Cauchy Problem for Fractional ODEs -- 4.1 Gronwall's Inequalities -- 4.2 ODEs with a Riemann-Liouville Fractional Derivative -- 4.3 ODEs with a Djrbashian-Caputo Fractional Derivative -- 5 Boundary Value Problem for Fractional ODEs -- 5.1 Green's Function -- 5.1.1 Riemann-Liouville case -- 5.1.2 Djrbashian-Caputo case -- 5.2 Variational Formulation -- 5.2.1 One-sided fractional derivatives -- 5.2.2 Two-sided mixed fractional derivatives -- 5.3 Fractional Sturm-Liouville Problem -- 5.3.1 Riemann-Liouville case -- 5.3.2 Djrbashian-Caputo case -- Part III Time-Fractional Diffusion -- 6 Subdiffusion: Hilbert Space Theory -- 6.1 Existence and Uniqueness in an Abstract Hilbert Space -- 6.2 Linear Problems with Time-Independent Coefficients -- 6.2.1 Solution representation -- 6.2.2 Existence, uniqueness and regularity -- 6.3 Linear Problems with Time-Dependent Coefficients -- 6.4 Nonlinear Subdiffusion -- 6.4.1 Lipschitz nonlinearity -- 6.4.2 Allen-Cahn equation. 327 $a6.4.3 Compressible Navier-Stokes problem -- 6.5 Maximum Principles -- 6.6 Inverse Problems -- 6.6.1 Backward subdiffusion -- 6.6.2 Inverse source problems -- 6.6.3 Determining fractional order -- 6.6.4 Inverse potential problem -- 6.7 Numerical Methods -- 6.7.1 Convolution quadrature -- 6.7.2 Piecewise polynomial interpolation -- 7 Subdiffusion: Ho?lder Space Theory -- 7.1 Fundamental Solutions -- 7.1.1 Fundamental solutions -- 7.1.2 Fractional ?-functions -- 7.2 Ho?lder Regularity in One Dimension -- 7.2.1 Subdiffusion in mathbbR -- 7.2.2 Subdiffusion in mathbbR+ -- 7.2.3 Subdiffusion on bounded intervals -- 7.3 Ho?lder Regularity in Multi-Dimension -- 7.3.1 Subdiffusion in mathbbRd -- 7.3.2 Subdiffusion in mathbbRd+ -- 7.3.3 Subdiffusion on bounded domains -- A Mathematical Preliminaries -- A.1 AC Spaces and Ho?lder Spaces -- A.1.1 AC spaces -- A.1.2 Ho?lder spaces -- A.2 Sobolev Spaces -- A.2.1 Lebesgue spaces -- A.2.2 Sobolev spaces -- A.2.3 Fractional Sobolev spaces -- A.2.4 s(?) spaces -- A.2.5 Bochner spaces -- A.3 Integral Transforms -- A.3.1 Laplace transform -- A.3.2 Fourier transform -- A.4 Fixed Point Theorems -- References -- References -- Index. 410 0$aApplied Mathematical Sciences 606 $aFractional differential equations 606 $aEquacions diferencials$2thub 608 $aLlibres electrònics$2thub 615 0$aFractional differential equations. 615 7$aEquacions diferencials 676 $a515.35 700 $aJin$b Bangti$0851643 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466415303316 996 $aFractional Differential Equations$91921875 997 $aUNISA