03308nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001700186072001700203072002300220072001600243100008300259245013400342250001800476264007200494300006600566336002600632337002600658338003600684347002400720505055400744520108301298650002502381650002802406650003902434650002802473700007702501710003402578773002602612776003602638776003602674776003602710856004602746912001402792912001502806999001702821978-981-99-2070-9DE-He21320251030112028.0cr nn 008mamaa240503s2024    si |    s    |||| 0|eng d  a97898199207099978-981-99-2070-97 a10.1007/978-981-99-2070-92doi 4aTJ212-225 7aTJFM2bicssc 7aGPFC2bicssc 7aTEC0070002bisacsh 7aTJFM2thema1 aXue, Dingyü.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut94124110aFractional Calculush[electronic resource] :bHigh-Precision Algorithms and Numerical Implementations /cby Dingyü Xue, Lu Bai.  a1st ed. 2024. 1aSingapore :bSpringer Nature Singapore :bImprint: Springer,c2024.  aXI, 406 p. 169 illus., 164 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aIntroduction to Fractional Calculus -- Commonly Used Special Functions: Definitions and Computing -- Definitions and Numerical Evaluations of Fractional Calculus -- High-precision Numerical Algorithms and Implementation in Fractional Calculus -- Approximations of Fractional-order Operators and Systems -- Analytical and Numerical Solutions of Linear Fractional-order Differential Equations -- Numerical Solutions of Nonlinear FODEs -- Block Diagram based Solutions of FODEs -- Numerical Solutions of Special Fractional-order Differential Equations.  aFractional calculus and its applications are fascinating research areas in many engineering disciplines. This book is a comprehensive collection of research from the author's group, which is one of the most active in the fractional calculus community worldwide and is the birthplace of one of the four MATLAB toolboxes in fractional calculus, the FOTF Toolbox. The book presents high-precision solution algorithms for a variety of fractional-order differential equations, including nonlinear, delay, and boundary value equations. Currently, there are no other universal solvers available for the latter two types of equations. Through this book, readers can systematically study the mathematics and solution methods in the field of fractional calculus and apply these concepts to different engineering fields, particularly control systems engineering This book is a translation of an original Chinese edition. The translation of some chapters was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done. 0aControl engineering. 0aDifferential equations.14aControl and Systems Theory.96586824aDifferential Equations.1 aBai, Lu.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9679642 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978981992069308iPrinted edition:z978981992071608iPrinted edition:z978981992072340uhttps://doi.org/10.1007/978-981-99-2070-9  aZDB-2-SMA  aZDB-2-SXMS  c59653d59653