LEADER 03100nam 22005055 450 001 9910855383603321 005 20240701122838.0 010 $a981-9920-70-1 024 7 $a10.1007/978-981-99-2070-9 035 $a(MiAaPQ)EBC31319201 035 $a(Au-PeEL)EBL31319201 035 $a(CKB)31918631300041 035 $a(DE-He213)978-981-99-2070-9 035 $a(EXLCZ)9931918631300041 100 $a20240503d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFractional Calculus $eHigh-Precision Algorithms and Numerical Implementations /$fby Dingyü Xue, Lu Bai 205 $a1st ed. 2024. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2024. 215 $a1 online resource (413 pages) 311 $a981-9920-69-8 327 $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. 330 $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. 606 $aAutomatic control 606 $aDifferential equations 606 $aControl and Systems Theory 606 $aDifferential Equations 615 0$aAutomatic control. 615 0$aDifferential equations. 615 14$aControl and Systems Theory. 615 24$aDifferential Equations. 676 $a518.1 700 $aXue$b Dingyu?$0633746 702 $aBai$b Lu 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910855383603321 996 $aFractional Calculus$94266469 997 $aUNINA