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020 _a9780429284083
_q(electronic bk.)
020 _a042928408X
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020 _a9780429811531
_q(electronic bk. : PDF)
020 _a0429811535
_q(electronic bk. : PDF)
020 _a9780429811524
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020 _a0429811527
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020 _a9780429811517
_q(electronic bk. : Mobipocket)
020 _a0429811519
_q(electronic bk. : Mobipocket)
020 _z9781138336162
020 _z1138336165
035 _a(OCoLC)1101422803
035 _a(OCoLC-P)1101422803
050 4 _aQA314
_b.Y36 2019eb
072 7 _aMAT
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072 7 _aMAT
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072 7 _aMAT
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072 7 _aPB
_2bicssc
082 0 4 _a515/.83
_223
100 1 _aYang, Xiao-Jun
_c(Mathematician),
_eauthor.
245 1 0 _aGeneral fractional derivatives :
_btheory, methods, and applications /
_cXiao-Jun Yang.
264 1 _aBoca Raton :
_bCRC Press, Taylor & Francis Group,
_c2019.
300 _a1 online resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
520 _aGeneral Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.
505 0 _aCover; Half Title; Title Page; Copyright Page; Dedication; Contents; Preface; Author; 1. Introduction; 1.1 History of fractional calculus; 1.1.1 The contribution for fractional calculus and applications; 1.1.2 The contribution for generalized fractional calculus and applications; 1.2 History of special functions; 1.3 Special functions with respect to another function; 2. Fractional Derivatives of Constant Order and Applications; 2.1 Fractional derivatives within power-law kernel; 2.2 Riemann-Liouville fractional calculus; 2.2.1 Riemann-Liouville fractional integrals
505 8 _a2.2.2 Riemann-Liouville fractional derivatives2.2.3 Riemann-Liouville fractional derivatives of a purely imaginary order; 2.3 Liouville-Sonine-Caputo fractional derivatives; 2.3.1 Motivations; 2.3.2 Liouville-Sonine-Caputo fractional derivatives; 2.4 Liouville-Grüunwald-Letnikov fractional derivatives; 2.4.1 Motivations; 2.4.2 Liouville-Grüunwald-Letnikov fractional derivatives; 2.4.3 Kilbas-Srivastava-Trujillo fractional derivatives; 2.5 Tarasov type fractional derivatives; 2.5.1 Tarasov type fractional derivatives; 2.5.2 Extended Tarasov type fractional derivatives
505 8 _a2.6 Riesz fractional calculus2.7 Feller fractional calculus; 2.8 Richard fractional calculus; 2.9 Erdélyi-Kober type fractional calculus; 2.9.1 Erdélyi-Kober type operators of fractional integration and fractional derivative; 2.9.2 Fractional integrals and fractional derivatives of the Erdélyi-Kober-Riesz, Erdélyi-Kober-Feller and Erdélyi-Kober-Rich; 2.10 Katugampola fractional calculus; 2.10.1 Katugampola fractional integrals and Katugampola fractional derivatives; 2.10.2 Katugampola type fractional integrals and Katugampola type fractional derivatives involving the exponential function
505 8 _a2.11 Hadamard fractional calculus2.11.1 Hadamard fractional integrals and fractional derivatives; 2.11.2 Hadamard type fractional integrals and fractional derivatives; 2.12 Marchaud fractional derivatives; 2.13 Tempered fractional calculus; 2.13.1 Motivations; 2.13.2 Tempered fractional derivatives; 2.13.3 Tempered fractional derivatives with respect to another function; 2.13.4 Tempered fractional derivatives of a purely imaginary order; 2.13.5 Tempered fractional integrals; 2.13.6 Tempered fractional integrals of a purely imaginary order
505 8 _a2.13.7 Tempered fractional derivatives in the sense of Liouville-Sonine and Liouville-Sonine-Caputo types2.13.8 Tempered fractional derivatives involving power-sine and power-cosine functions; 2.13.9 Tempered fractional calculus involving power-Kohlrausch-Williams-Watts function; 2.13.9.1 Tempered fractional derivative in the Liouville-SonineCaputo type involving the kernel of the power-Kohlrausch-Williams-Watts function; 2.13.9.2 Tempered fractional integral involving the kernel of the power-Kohlrausch-Williams-Watts function; 2.13.10 Sabzikar-Meerschaert-Chen tempered fractional calculus
588 _aOCLC-licensed vendor bibliographic record.
650 0 _aFractional calculus.
650 0 _aCalculus.
650 7 _aMATHEMATICS / General
_2bisacsh
650 7 _aMATHEMATICS / Applied
_2bisacsh
650 7 _aMATHEMATICS / Arithmetic
_2bisacsh
856 4 0 _3Read Online
_uhttps://www.taylorfrancis.com/books/9780429284083
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
942 _2lcc
_cEBK
999 _c17437
_d17437