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Books on the topic 'Fractional Difference'

Author: Grafiati

Published: 4 June 2025

Last updated: 15 July 2025

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1

Ferreira, Rui A. C. Discrete Fractional Calculus and Fractional Difference Equations. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-92724-0.

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2

Annaby, Mahmoud H. q-Fractional Calculus and Equations. Springer Berlin Heidelberg, 2012.

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3

Abbas, Saïd. Topics in Fractional Differential Equations. Springer New York, 2012.

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4

Ahlbrandt, Calvin D. Discrete Hamiltonian systems: Difference equations, continued fractions, and Riccati equations. Kluwer Academic Publishers, 1996.

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5

Ferreira, Rui A. C. Discrete Fractional Calculus and Fractional Difference Equations. Springer International Publishing AG, 2022.

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6

Sun, Zhi-zhong, China Science Publishing &. Media China Science Publishing &. Media Ltd, and Guang-hua Gao. Fractional Differential Equations: Finite Difference Methods. de Gruyter GmbH, Walter, 2020.

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7

Sun, Zhi-zhong, China Science Publishing & Media China Science Publishing & Media Ltd., and Guang-hua Gao. Fractional Differential Equations: Finite Difference Methods. de Gruyter GmbH, Walter, 2020.

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8

Sun, Zhi-zhong, China Science Publishing & Media China Science Publishing & Media Ltd., and Guang-hua Gao. Fractional Differential Equations: Finite Difference Methods. de Gruyter GmbH, Walter, 2020.

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9

Ortigueira, Manuel Duarte, and Duarte Valério. Fractional Signals and Systems. de Gruyter GmbH, Walter, 2020.

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10

Ortigueira, Manuel Duarte, and Duarte Valério. Fractional Signals and Systems. de Gruyter GmbH, Walter, 2021.

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11

Ortigueira, Manuel Duarte, and Duarte Valério. Fractional Signals and Systems. de Gruyter GmbH, Walter, 2020.

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12

Ortigueira, Manuel Duarte, and Duarte Valério. Fractional Signals and Systems. de Gruyter GmbH, Walter, 2020.

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13

Umarov, Sabir. Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols. Springer, 2016.

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14

Umarov, Sabir. Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols. Springer International Publishing AG, 2015.

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15

Umarov, Sabir. Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols. Springer London, Limited, 2015.

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16

Salim, Abdelkrim. Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability. Elsevier Science & Technology Books, 2024.

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17

Salim, Abdelkrim. Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability. Elsevier Science & Technology, 2024.

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18

Tarasova, Valentina V., and Vasily E. Tarasov. Economic Dynamics with Memory: Fractional Calculus Approach. de Gruyter GmbH, Walter, 2021.

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19

Tarasova, Valentina V., and Vasily E. Tarasov. Economic Dynamics with Memory: Fractional Calculus Approach. de Gruyter GmbH, Walter, 2021.

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20

Tarasova, Valentina V., and Vasily E. Tarasov. Economic Dynamics with Memory: Fractional Calculus Approach. de Gruyter GmbH, Walter, 2021.

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21

N'Guérékata, Gaston M., Saïd Abbas, and Mouffak Benchohra. Topics in Fractional Differential Equations. Springer, 2012.

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22

N'Guérékata, Gaston M., Saïd Abbas, and Mouffak Benchohra. Topics in Fractional Differential Equations. Springer New York, 2014.

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23

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations. Elsevier, 2016. http://dx.doi.org/10.1016/c2014-0-04797-1.

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24

Henderson, Johnny, and Rodica Luca. Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions. Elsevier Science & Technology Books, 2015.

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25

Henderson, Johnny, and Rodica Luca. Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions. Elsevier Science & Technology Books, 2015.

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26

Ahlbrandt, Calvin. Discrete Hamiltonian Systems: "Difference Equations, Continued Fractions, And Riccati Equations". Springer, 2010.

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27

Peterson, A. C., and Calvin Ahlbrandt. Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations. Springer, 2013.

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28

Rigo, Fausto, Covadonga Fernández-Golfín, and Bruno Pinamonti. Dilated cardiomyopathy. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780198726012.003.0043.

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Dilated cardiomyopathy (DCM) is characterized by a globally dilated and dysfunctioning left ventricle (LV). Therefore, echocardiographic diagnostic criteria for DCM are a LV end-diastolic diameter greater than 117% predicted value corrected for age and body surface area and a LV ejection fraction less than 45% (and/or fractional shortening less than 25%). Usually, the LV is also characterized by a normal or mildly increased wall thickness with eccentric hypertrophy and increased mass, a spherical geometry (the so-called LV remodelling), a dyssynchronous contraction (typically with left bundle

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29

Speeckaert, Marijn, and Joris Delanghe. Tubular function. Edited by Christopher G. Winearls. Oxford University Press, 2015. http://dx.doi.org/10.1093/med/9780199592548.003.0008.

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Assessment of tubular function is more complicated than the measurement of glomerular filtration rate. Different functions may be affecting according to the different segments of tubule involved. Key tests include concentrating and diluting capacity, and fractional excretion of sodium. Tubular proteinuria occurs when glomerular function is normal, but when the proximal tubules have a diminished capacity to reabsorb and to catabolize proteins, causing an increased urinary excretion of the low-molecular-mass proteins that normally pass through the glomerulus. Proximal tubular dysfunction is char

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30

Ray, Sumantra (Shumone), Sue Fitzpatrick, Rajna Golubic, Susan Fisher, and Sarah Gibbings, eds. Navigating research methods: quantitative and clinical/epidemiological methods. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780199608478.003.0003.

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This chapter focuses on various types of study design used in clinical and healthcare research with an emphasis on observational studies whilst randomised controlled trials are explained in Chapter 15. Within observational studies, the distinction between descriptive and analytical studies is made and different sources of error in epidemiological studies are reviewed. Main features, advantages and disadvantages of analytical observational studies are described for the following designs: ecological studies, cohort studies, case-control studies and cross-sectional studies. A brief overview of ex

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31

Walsh, Bruce, and Michael Lynch. Using Molecular Data to Detect Selection: Signatures from Multiple Historical Events. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198830870.003.0010.

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This chapter examines the search for a pattern of repetitive adaptive substitutions over evolutionary time. In contrast with the previous chapter, only a modest number of tests toward this aim have been proposed. The HKA and McDonald-Kreitman tests contrast the polymorphism to divergence ratio between different genomic classes (such as different genes or silent versus replacement sites within the same gene). These approaches can detect an excess of substitutions, which allows one to estimate the fraction of adaptive sites. This chapter reviews the empirical data on estimates of this fraction a

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32

Caraballo Carmona, Carlos Manuel, and Francisco Lázaro García Fernández. Methodology of Mathematics Teaching. Treatment to School Mathematics Equations. Editorial Tecnocientífica Americana, 2021. http://dx.doi.org/10.51736/eta2021edu1.

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This book is aimed at pre-university students and its purpose is to contribute to the development of their knowledge related to the algebraic and transcendent equations studied at school, as well as their application to different situations that occur in practice in an innovative and creative way, using the procedures for solving them, so that it allows the consolidation of attitudes such as industriousness, responsibility and science. The system of knowledge worked on and treated didactically in this book is related to the algebraic equations and within them the linear, quadratic, fractional

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33

Stroud, Barry. Concepts of Colour and Limits of Understanding. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198809753.003.0016.

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This chapter examines some puzzling reflections by Ludwig Wittgenstein on the possibility of understanding concepts of the colours of things different from those already familiar to us. It begins with a discussion of Wittgenstein’s statement: ‘Someone who has perfect pitch can learn a language-game that I cannot learn’. In particular, it considers how Wittgenstein draws a connection between perfect pitch and concepts of colours and invites us to imagine people who speak of colours intermediate between red and yellow by means of fractions in a kind of binary notation representing different prop

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34

Aldridge, Irene. Can Humans Dance with Machines? Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190269999.003.0027.

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This chapter examines high-frequency trading (HFT), including core groups of strategies and resulting impacts. Using order-by-order market data analysis, the chapter shows that much of what is often construed to be useless noise of order cancellations actually represents meaningful order revisions, part of the real-time market bargaining. The chapter further shows that a small fraction of the order cancellations are a product of purely toxic liquidity. Market participants of different frequencies tend to react differently to such toxic orders, with higher-frequency traders largely ignoring and

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35

Bianconi, Ginestra. Classical Percolation, Generalized Percolation and Cascades. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198753919.003.0012.

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This chapter characterizes the robustness of multiplex and multilayer networks using classical percolation, directed percolation and antagonistic percolation. Classical percolation determines whether a finite fraction of nodes of the multilayer networks are connected by any type of connection. Classical percolation can be affected by multiplexity since the degree correlations among different layers can modulate the robustness of the entire multilayer network. Directed percolation describes the propagation of a disease requiring cooperative infection from different layers of the multiplex netwo

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36

Bianconi, Ginestra. Interdependent Multilayer Networks. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198753919.003.0011.

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This chapter characterizes interdependent multilayer networks and their increased fragility. Interdependent networks are stylized models that can represent different complex systems, ranging from global infrastructures to molecular networks in the cell. When a fraction of nodes is initially damaged, interdependent networks are affected by dramatic cascades of failures that suddenly dismantle the multilayer network. The theory beyond this phenomenology is discussed in a pedagogical way by characterizing the percolation, discontinuous and hybrid transitions. The interplay between structure and f

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37

Hornigold, Judy, and Rose Jewell. GCSE Maths for Neurodivergent Learners. Jessica Kingsley Publishers, 2022. http://dx.doi.org/10.5040/9781805016069.

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We all have to take GCSE maths, but that doesn't mean we all find it easy! If you have been struggling with maths and find working with numbers particularly tough, this is the go-to GCSE maths study guide to help you ace your exams. This is the first GCSE maths study guide (covering number, proportion and algebra) that uses engaging multisensory methods of learning for students with specific learning differences. It offers unique insight into why you may find maths extra challenging and gives practical advice on how you can adapt your studying processes to suit the way that you learn best. Wit

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38

Paneni, Francesco, and Massimo Volpe. Co-morbidity (HFrEF and HFpEF): hypertension. Oxford University Press, 2019. http://dx.doi.org/10.1093/med/9780198784906.003.0415_update_001.

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Hypertensive heart disease is a major cause of heart failure (HF) and mortality. Hypertension precedes HF occurrence in 75% of cases, and carries a sixfold increase in HF risk as compared to non-hypertensive individuals. Most importantly, a minority of patients survive 5 years after the onset of hypertensive HF. In hypertensive patients, the heart may present different patterns of adaptive remodelling: concentric remodelling, concentric hypertrophy, and eccentric hypertrophy. Although most hypertensive patients are at high risk of developing concentric hypertrophy, a growing proportion of subj

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39

Crous-Bou, Marta, Immaculata de Vivo, and Pagona Lagiou. Endometrial Cancer. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190676827.003.0018.

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Lifestyle factors contribute appreciably to endometrial cancer risk, with obesity accounting for over one-third of incident cases in high-income societies. Unlike cervical cancer, which is a model of viral carcinogenesis, endometrial cancer is considered a model of hormonal carcinogenesis, as use of unopposed estrogens postmenopausally and obesity are the best-established risk factors. Endometrial cancer is also the only known malignancy for which cigarette smoking has been shown to confer protection. Risk reduction conferred by current smoking, past oral contraceptive use, childbearing, and p

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40

Branch, Ben S. If You're So Smart, Why Aren't You Rich? Praeger, 2006. http://dx.doi.org/10.5040/9798400668272.

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Football is often described as a game of inches. First downs, scoring, and in/out of bound decisions that can determine the outcome of the game may even come down to fractions of an inch. Investing is similar: the difference between outperforming or underperforming the market may be a few fractions of a percentage point. As Ben Branch succinctly states, successful investing, defined as outperforming the market averages, is not easy. And yet it is very much a game worth playing, particularly if you win. The key to being on the winning side is to understand the fundamental principles of investin

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41

Neuman, Susan B. Changing the Odds for Children at Risk. Greenwood Publishing Group, Inc., 2008. http://dx.doi.org/10.5040/9798400624575.

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Schools, today, are in the midst of the most major, costly educational reform movement in their history as they grapple with the federal mandates to leave no children behind, says author Susan B. Neuman, former Assistant Secretary for Elementary and Secondary Education under President George W. Bush. Although some efforts for investing resources will be substantially more productive than others, there is little evidence that, despite many heroic attempts to beat the odds, any of these efforts will close more than a fraction of the differences in achievement for poor minority children and their

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42

Shinoda, Tomohito. Leading Japan. Praeger, 2000. http://dx.doi.org/10.5040/9798400677731.

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Shinoda provides an analytical framework for examining the role of the prime minister in Japan's political decision making. He shows that two dimensions of fraction within the government and the ruling party—interagency rivalry and intraparty factions—confront the prime minister whenever a major policy issue needs to be resolved. Despite these obstacles, Shinoda shows that the prime minister can be effective. First, Shinoda identifies the sources of power available to Japanese prime ministers—some from legal authorities and others from informal sources. Because prime ministers must rely on inf

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43

Fitzsimmons, Michael P. The Place of Words. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780190644536.001.0001.

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From its initial appearance in 1694 and through successive editions in 1718, 1740, and 1762, the Dictionnaire de l’Académie Française had risen to become the definitive arbiter of the French language. Preparation of the fifth edition was at an advanced state when the French Revolution began in 1789 but it remained unfinished when the National Convention suppressed academies in August 1793. Seeking to codify the language of the Revolution, the Convention commissioned two Parisian publishers to complete the fifth edition, hoping that it would be a vehicle for promoting the ideals of the Revoluti

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44

Farmakis, Dimitrios, John Parissis, and Gerasimos Filippatos. Acute heart failure: epidemiology, classification, and pathophysiology. Oxford University Press, 2015. http://dx.doi.org/10.1093/med/9780199687039.003.0051.

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Acute heart failure is defined as the rapid development or change of symptoms and signs of heart failure that requires urgent medical attention and usually hospitalization. Acute heart failure is the first reason for hospital admission in individuals aged 65 or more and accounts for nearly 70% of the total health care expenditure for heart failure. It is characterized by an adverse prognosis, with an in-hospital mortality rate of 4-7%, a 2-3-month post-discharge mortality of 7-11%, and a 2-3-month readmission rate of 25-30%. The majority of patients have a previous history of heart failure and

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45

Kucharski, Fred, and Muhammad Adnan Abid. Interannual Variability of the Indian Monsoon and Its Link to ENSO. Oxford University Press, 2017. http://dx.doi.org/10.1093/acrefore/9780190228620.013.615.

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The interannual variability of Indian summer monsoon is probably one of the most intensively studied phenomena in the research area of climate variability. This is because even relatively small variations of about 10% to 20% from the mean rainfall may have dramatic consequences for regional agricultural production. Forecasting such variations months in advance could help agricultural planning substantially. Unfortunately, a perfect forecast of Indian monsoon variations, like any other regional climate variations, is impossible in a long-term prediction (that is, more than 2 weeks or so in adva

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46

Browne-Miller, Angela. To Have and To Hurt. Praeger, 2007. http://dx.doi.org/10.5040/9798216026167.

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Every year, nearly 2 million injuries and some 1,300 deaths result from so-called intimate partner violence. In this work, psychotherapist Browne-Miller uses vignettes, as well as standing and emerging research, to detail both healthy and hurtful relationships and to show partners how to recognize and change relationships on, or headed toward, the path to abuse. She also explains when to leave a relationship, as well as how to do that so as to disentangle without further harm. This is a book that will interest not only those involved in, or who know of someone who is or might be involved in, a

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