Fractional Calculus for Scientists and Engineers

By Manuel Duarte Ortigueira. Lecture Notes in Electrical Engineering, 2011

754 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/3497f5d7765206b8937383a8e20f4a3df17fb4d9

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Citations in the corpus

The Chronicles of Fractional Calculus (2017, neutral): “2009 [6, 90, 122, 27, 89, 77, 155] [109, 17] 2010 [111, 31, 133, 165, 46] [98, 106, 63] 2011 [156, 144, 87, 65, 126, 92, 3, 187, 207, 78, 44, 93] [86, 18]”
A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors (2018, background): “A thorough exposition of FOC can be found in textbooks on fractional-order system modeling, analysis, and applications [19, 20, 21] and related survey articles [22, 23].”
Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015, result): “We have taken the present occasion, as a compliment to our previous survey [107], to cite books published during the years 2011 [92, 80, 44, 26, 65, 47, 5, 106, 117], 2012 [7, 3, 77, 1, 51, 38, 102, 56, 122, 15, 112, 110, 118], 2013 [14, 18, 89, 29, 36], and 2014 [57, 4, 121, 39, 105, 40, 66, 86, 2,”
Fractional-order models of supercapacitors, batteries and fuel cells: a survey (2015, methodology): “where voðtÞ is the time domain output voltage and Ea;bð Þ is the two-term Mittag-Leffler function defined as [3]”
A Gronwall inequality for a general Caputo fractional operator (2017, background): “ction Fractional calculus is an important subject with numerous applications to diﬀerent ﬁelds outside mathematics like physics [8, 21, 29], chemistry [4, 5, 14], biology [3, 20, 27, 30], engineering [9, 10, 24, 28], etc. It allows us to deﬁne derivatives and integrals of non-integer order, which ma”
A fractional calculus approach to the dynamic optimization of biological reactive systems. Part I: Fractional models for biological reactions (2014, methodology): “Theoretical developments are also in progress (Diethelm, 2010; Ortigueira, 2011) in order to consolidate the fundamentals and provide the basis for a more extensive use of this tool in science and engineering.”
Existence and Ulam stability for nonlinear implicit fractional differential equations with Hadamard derivative (2017, background): “We refer the reader, for example, to the books such as [6, 18, 20, 22, 30], and references therein.”
Science metrics on fractional calculus development since 1966 (2013, background): “Figure 2 (left) depicts the evolution of Da [19, 12, 56, 75, 57, 99, 60, 87, 100, 100, 77, 68, 85, 95, 69, 70, 71, 72, 78, 23, 102, 13, 96, 64, 114, 36, 79, 73, 91, 63, 84, 80, 105, 109, 4, 111, 82, 22, 27, 28, 110, 81, 67, 32, 29, 86, 52, 33, 117, 106, 55, 58, 112, 113, 108, 6, 15, 2, 41, 59, 10, 4”
Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order (2015, background): “See, for example, the books ([2, 3, 6, 9, 10, 24, 25]), the papers [4, 5, 11] and the references therein.”
On stability for nonlinear implicit fractional differential equations (2015, neutral): “See, for example, the books such as [2–4, 7, 27, 31, 37] and the articles [9, 10], and references therein.”