소장자료
LDR | 05105cam a2200000 a | ||
001 | 0100582355▲ | ||
003 | OCoLC▲ | ||
005 | 20221208133857▲ | ||
007 | ta ▲ | ||
008 | 210905s2021 sz a b 001 0 eng c▲ | ||
020 | ▼a9783030760427▼q(hbk.)▲ | ||
020 | ▼a3030760421▼q(hbk.)▲ | ||
020 | ▼z9783030760434▼q(ebk.)▲ | ||
040 | ▼aLWU▼beng▼cLWU▼dOCLCO▼dYDX▼dBDX▼dOHX▼dPAU▼dOCLCO▼dYDX▼dOCLCF▼dUKMGB▼dSTF▼dOCLCQ▼dOCLCO▼d221016▲ | ||
082 | 0 | 4 | ▼a515/.35▼223▲ |
090 | ▼a515.35▼bJ61f▲ | ||
100 | 1 | ▼aJin, Bangti.▲ | |
245 | 1 | 0 | ▼aFractional differential equations :▼ban approach via fractional derivatives /▼cBangti Jin.▲ |
260 | ▼aCham, Switzerland :▼bSpringer,▼c[2021]▲ | ||
300 | ▼axiv, 368 p. :▼bill. ;▼c25 cm▲ | ||
490 | 0 | ▼aApplied mathematical sciences,▼x0066-5452 ;▼vv. 206▲ | |
504 | ▼aIncludes bibliographical references and index.▲ | ||
505 | 0 | 0 | ▼gPreliminaries --▼tContinuous Time Random Walk --▼tRandom Walk on a Lattice --▼tContinuous Time Random Walk --▼tSimulating Continuous Time Random Walk --▼tFractional Calculus --▼tGamma Function --▼tRiemann-Liouville Fractional Integral --▼tFractional Derivatives --▼tRiemann-Liouville fractional derivative --▼tDjrbashian-Caputo fractional derivative --▼tGr|nwald-Letnikov fractional derivative --▼tMittag-Leffler and Wright Functions --▼tMittag-Leffler Function --▼tBasic analytic properties --▼tMittag-Leffler function E ... --▼tWright Function --▼tBasic analytic properties --▼tWright function W ... --▼tNumerical Algorithms --▼tMittag-Leffler function E ... --▼tWright function W ... --▼tFractional Ordinary Differential Equations --▼tCauchy Problem for Fractional ODEs --▼tGronwall's Inequalities --▼tODEs with a Riemann-Liouville Fractional Derivative --▼tODEs with a Djrbashian-Caputo Fractional Derivative --▼tBoundary Value Problem for Fractional ODEs --▼tGreen's Function --▼tRiemann-Liouville case --▼tDjrbashian-Caputo case --▼tVariational Formulation --▼tOne-sided fractional derivatives --▼tTwo-sided mixed fractional derivatives --▼tFractional Sturm-Liouville Problem --▼tRiemann-Liouville case --▼tDjrbashian-Caputo case --▼tTime-Fractional Diffusion --▼tSubdiffusion : Hilbert Space Theory --▼tExistence and Uniqueness in an Abstract Hilbert Space --▼tLinear Problems with Time-Independent Coefficients --▼tSolution representation --▼tExistence, uniqueness and regularity --▼tLinear Problems with Time-Dependent Coefficients --▼tNonlinear Subdiffusion --▼tLipschitz nonlinearity --▼tAllen-Cahn equation --▼tCompressible Navier-Stokes problem --▼tMaximum Principles --▼tInverse Problems --▼tBackward subdiffusion --▼tInverse source problems. --▼tDetermining fractional order --▼tInverse potential problem --▼tNumerical Methods --▼tConvolution quadrature --▼tPiecewise polynomial interpolation --▼tSubdiffusion : H̲lder Space Theory --▼tFundamental Solutions --▼tFundamental solutions --▼tFractional ... -functions --▼tH̲lder Regularity in One Dimension --▼tSubdiffusion in R --▼tSubdiffusion in R₊ --▼tSubdiffusion on bounded intervals --▼tH̲lder Regularity in Multi-Dimension --▼tSubdiffusion in R ... --▼tSubdiffusion in R ... ₊ --▼tSubdiffusion on bounded domains --▼tMathematical Preliminaries --▼tAC Spaces and H̲lder Spaces --▼tAC spaces --▼tH̲lder spaces --▼tSobolev Spaces --▼tLebesgue spaces --▼tSobolev spaces --▼tFractional Sobolev spaces --▼tH⁵ (...) spaces --▼tBochner spaces --▼tIntegral Transforms --▼tLaplace transform --▼tFourier transform --▼tFixed Point Theorems --▼gReferences --▼gIndex.▲ |
520 | ▼aThis graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.▲ | ||
650 | 0 | ▼aFractional differential equations.▲ |
Fractional differential equations : an approach via fractional derivatives
자료유형
국외단행본
서명/책임사항
Fractional differential equations : an approach via fractional derivatives / Bangti Jin.
개인저자
발행사항
Cham, Switzerland : Springer , [2021]
형태사항
xiv, 368 p. : ill. ; 25 cm
총서사항
Applied mathematical sciences , 0066-5452 ; v. 206
서지주기
Includes bibliographical references and index.
내용주기
Preliminaries -- Continuous Time Random Walk -- Random Walk on a Lattice -- Continuous Time Random Walk -- Simulating Continuous Time Random Walk -- Fractional Calculus -- Gamma Function -- Riemann-Liouville Fractional Integral -- Fractional Derivatives -- Riemann-Liouville fractional derivative -- Djrbashian-Caputo fractional derivative -- Gr|nwald-Letnikov fractional derivative -- Mittag-Leffler and Wright Functions -- Mittag-Leffler Function -- Basic analytic properties -- Mittag-Leffler function E ... -- Wright Function -- Basic analytic properties -- Wright function W ... -- Numerical Algorithms -- Mittag-Leffler function E ... -- Wright function W ... -- Fractional Ordinary Differential Equations -- Cauchy Problem for Fractional ODEs -- Gronwall's Inequalities -- ODEs with a Riemann-Liouville Fractional Derivative -- ODEs with a Djrbashian-Caputo Fractional Derivative -- Boundary Value Problem for Fractional ODEs -- Green's Function -- Riemann-Liouville case -- Djrbashian-Caputo case -- Variational Formulation -- One-sided fractional derivatives -- Two-sided mixed fractional derivatives -- Fractional Sturm-Liouville Problem -- Riemann-Liouville case -- Djrbashian-Caputo case -- Time-Fractional Diffusion -- Subdiffusion : Hilbert Space Theory -- Existence and Uniqueness in an Abstract Hilbert Space -- Linear Problems with Time-Independent Coefficients -- Solution representation -- Existence, uniqueness and regularity -- Linear Problems with Time-Dependent Coefficients -- Nonlinear Subdiffusion -- Lipschitz nonlinearity -- Allen-Cahn equation -- Compressible Navier-Stokes problem -- Maximum Principles -- Inverse Problems -- Backward subdiffusion -- Inverse source problems. -- Determining fractional order -- Inverse potential problem -- Numerical Methods -- Convolution quadrature -- Piecewise polynomial interpolation -- Subdiffusion : H̲lder Space Theory -- Fundamental Solutions -- Fundamental solutions -- Fractional ... -functions -- H̲lder Regularity in One Dimension -- Subdiffusion in R -- Subdiffusion in R₊ -- Subdiffusion on bounded intervals -- H̲lder Regularity in Multi-Dimension -- Subdiffusion in R ... -- Subdiffusion in R ... ₊ -- Subdiffusion on bounded domains -- Mathematical Preliminaries -- AC Spaces and H̲lder Spaces -- AC spaces -- H̲lder spaces -- Sobolev Spaces -- Lebesgue spaces -- Sobolev spaces -- Fractional Sobolev spaces -- H⁵ (...) spaces -- Bochner spaces -- Integral Transforms -- Laplace transform -- Fourier transform -- Fixed Point Theorems -- References -- Index.
요약주기
This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.
ISBN
9783030760427 3030760421
청구기호
515.35 J61f
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