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1

Pskhu, A. V., and S. Sh Rekhviashvili. "Retarded Potentials in Fractional Electrodynamics." Moscow University Physics Bulletin 75, no. 4 (2020): 316–19. http://dx.doi.org/10.3103/s0027134920040098.

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2

Schiavone, S. E. "Fractional powers of the retarded potential." Applicable Analysis 42, no. 1-4 (1991): 145–55. http://dx.doi.org/10.1080/00036819108840038.

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3

Sikora, Beata. "Controllability criteria for time–delay fractional systems with a retarded state." International Journal of Applied Mathematics and Computer Science 26, no. 3 (2016): 521–31. http://dx.doi.org/10.1515/amcs-2016-0036.

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Abstract The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U-controllability are established and proved. Num
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4

Jiang, Wei, and Zheng Xia Wang. "Image Denoising New Method Based on Fractional Partial Differential Equation." Advanced Materials Research 532-533 (June 2012): 797–802. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.797.

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Current total variation method excels at denoising and keeping the characteristics of image edges. However, its ability to retain texture details of smoothing region of image is poor. By combining fractional-order differential theory with total variation method, a new image denoising method is proposed. The new method, while effectively inheriting these advantages, uses the fractional-order differential amplitude-frequency and effectively. Simulation results which we have got show that the new method, on the one hand, can better suppress noise, keep the characteristics of image edges, and reta
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5

Nguyen, Van Quang, and Suchin Arunsawatwong. "Stability and Stabilization of Retarded Fractional Delay Differential Systems." IFAC Proceedings Volumes 41, no. 2 (2008): 3928–33. http://dx.doi.org/10.3182/20080706-5-kr-1001.00661.

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6

Dhandapani, Prasantha Bharathi, Jayakumar Thippan, Dumitru Baleanu, and Vinoth Sivakumar. "On a novel fuzzy fractional retarded delay epidemic model." AIMS Mathematics 7, no. 6 (2022): 10122–42. http://dx.doi.org/10.3934/math.2022563.

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<abstract><p>The traditional compartmental epidemic models such as SIR, SIRS, SEIR consider mortality rate as a parameter to evaluate the population changes in susceptible, infected, recovered, and exposed. We present a modern model where population changes in mortality are also considered as the parameter. The existing models in epidemiology always construct a system of the closed medium in which they assume that new birth, as well as new death, will not be possible. But in real life, such a concept will not be assumed to not exist. From our wide observation, we find that the chan
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7

Tafesse, Simegne, and Nagarajan Sukavanam. "Approximate Controllability of Fractional Order Retarded Semilinear Control Systems." International Journal of Modern Nonlinear Theory and Application 02, no. 03 (2013): 153–60. http://dx.doi.org/10.4236/ijmnta.2013.23020.

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8

Subramanian, Shivaram, and Hanif D. Sherali. "A fractional programming approach for retail category price optimization." Journal of Global Optimization 48, no. 2 (2009): 263–77. http://dx.doi.org/10.1007/s10898-009-9491-2.

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9

Kim, Daewook, and Jin-Mun Jeong. "Controllability for Retarded Semilinear Neutral Control Systems of Fractional Order in Hilbert Spaces." Mathematics 9, no. 6 (2021): 671. http://dx.doi.org/10.3390/math9060671.

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In this paper, we discuss the approximate controllability for a class of retarded semilinear neutral control systems of fractional order by investigating the relations between the reachable set of the semilinear retarded neutral system of fractional order and that of its corresponding linear system. The research direction used here is to find the conditions for nonlinear terms so that controllability is maintained even in perturbations. Finally, we will show a simple example to which the main result can be applied.
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10

Wang, Ying, Jingxiao Jiang, Zhi Cai, and Kaifeng Zhang. "Fractional Prospect Theory-Based Bidding Strategy of Power Retail Company in the Uniform Pricing Electricity Market under Price Uncertainty." Fractal and Fractional 7, no. 3 (2023): 210. http://dx.doi.org/10.3390/fractalfract7030210.

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This paper first proposes a fractional prospect theory-based method for modeling the bidding strategy of a power retail company in the uniform pricing electricity market under price uncertainty. Different from the traditional methods which assume that the retail company always bids completely rationally to maximize its individual payoffs, this paper introduces the prospect theory (PT) into the bidding model to reflect the impacts of psychological factors and subjective perceptions. To address the partial uncertainties brought by the continuous probability distribution in the value function, th
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11

Usta, Fuat, and Mehmet Zeki Sarıkaya. "The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities." Demonstratio Mathematica 52, no. 1 (2019): 204–12. http://dx.doi.org/10.1515/dema-2019-0017.

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AbstractIn this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.
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12

Rajalakshmi, K., and T. Ramachandramoorthy. "Oxidation of Chalcones by Morpholinium Chlorochromate with Oxalic Acid as Catalyst: Kinetic and Mechanistic Study." Journal of Chemistry 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/240102.

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The kinetics of oxidation of chalcones by morpholinium chlorochromate (MCC) has been studied in 55% acetic acid-water (v/v) medium. The reaction showed unit order dependence each with respect to oxidant and catalyst and fractional order with respect to substrate and H+ion. Increased ionic strength has no effect on the reaction rate. In the case of substituted chalcones, the order with respect to substrate varies depending upon the nature of the substituent present in the ring. In general, the electron withdrawing substituents retard the reaction rate while the electron releasing substituents e
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13

Akgüller, Ömer, Mehmet Ali Balcı, Larissa Margareta Batrancea, Dilara Altan Koç, and Anca Nichita. "Neutral Delayed Fractional Models in Financial Time Series: Insights into Borsa Istanbul Sectors Affected by the Kahramanmaraş Earthquake." Fractal and Fractional 9, no. 3 (2025): 141. https://doi.org/10.3390/fractalfract9030141.

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This study examines the impact of the Kahramanmaraş Earthquake on four key sectors of Borsa Istanbul: Basic Metal, Insurance, Non-Metallic Mineral Products, and Wholesale and Retail Trade using neutral delayed fractional differential equations. Employing the Chebyshev collocation method, we numerically solved the neutral delayed fractional differential equations with initial conditions scaled by each sector’s log difference standard deviation to accurately reflect market volatility. Fractional orders were derived from the Hurst exponent, and time delays were identified using average mutual inf
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14

Zhang, Xuping, and Yongxiang Li. "Fractional Retarded Evolution Equations with Measure of Noncompactness Subjected to Mixed Nonlocal Plus Local Initial Conditions." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 1 (2018): 69–81. http://dx.doi.org/10.1515/ijnsns-2017-0098.

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AbstractWe consider the fractional retarded evolution equations $$^{C}D_{t}^{q}u(t)+Au(t)=f\Big(t,u_t,\int_{0}^{t}w(t,s,u_s)ds\Big),\quad t\in[0,a],$$where $^{C}D_{t}^{q}$, $q\in(0,1]$, is the fractional derivative in the Caputo sense, $-A$ is the infinitesimal generator of a $C_0$-semigroup of uniformly bounded linear operators $T(t)$$(t\geq0)$ on a Banach space $X$ and the nonlinear operators $f$ and $w$ are given functions satisfying some assumptions, subjected to a general mixed nonlocal plus local initial condition of the form $u(t)=g(u)(t)+\phi(t)$, $t\in[-h,0]$. Under more general condi
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15

Lan, Do, and Vu Nam Phong. "Decay solutions to retarded fractional evolution inclusions with superlinear perturbations." Fixed Point Theory 23, no. 1 (2022): 293–310. http://dx.doi.org/10.24193/fpt-ro.2022.1.19.

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16

Garrido-Atienza, María J., and Jianhua Huang. "Retarded Neutral Stochastic Equations Driven by Multiplicative Fractional Brownian Motion." Stochastic Analysis and Applications 32, no. 5 (2014): 820–39. http://dx.doi.org/10.1080/07362994.2014.938860.

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17

Bonnet, Catherine, and Jonathan R. Partington. "Analysis of fractional delay systems of retarded and neutral type." Automatica 38, no. 7 (2002): 1133–38. http://dx.doi.org/10.1016/s0005-1098(01)00306-5.

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18

Zheng, Guoliang, Lili Wan, Tiefeng He, Qingyang Wu, and Xuhui Zhang. "The Propagation Characteristics of Circular Airy Beams with Propagational Fractional-Order Optical Vortices." Photonics 11, no. 1 (2024): 64. http://dx.doi.org/10.3390/photonics11010064.

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We investigate the propagation properties of circular Airy beams (CABs) with propagational fractional-order optical vortices (OVs). The superposition of the phase singularity and polarization singularity from a vortex vector beam (VVB) plays a significant role in creating a propagational fractional vortex beam. Propagational fractional vortex beams can be considered as a superposition of left and right circularly polarized vortex beams with different integer topological charges (TCs). We study the propagation characteristics of two kinds of propagational fractional vortex CABs, and the results
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19

Abbas, Saïd, Mouffak Benchohra, and Seenith Sivasundaram. "Coupled Pettis-Hadamard Fractional Differential Systems with Retarded and Advanced Arguments." Journal of Mathematics and Statistics 14, no. 1 (2018): 56–63. http://dx.doi.org/10.3844/jmssp.2018.56.63.

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20

Cho, Seong Ho, Jin-Mun Jeong, and Yong Han Kang. "REGULARITY FOR FRACTIONAL ORDER RETARDED NEUTRAL DIFFERENTIAL EQUATIONS IN HILBERT SPACES." Journal of the Korean Mathematical Society 53, no. 5 (2016): 1019–36. http://dx.doi.org/10.4134/jkms.j150354.

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21

Zhang, Xuping, Pengyu Chen, and Yongxiang Li. "Fractional Retarded Differential Equations Involving Mixed Nonlocal Plus Local Initial Conditions." Numerical Functional Analysis and Optimization 40, no. 14 (2019): 1678–702. http://dx.doi.org/10.1080/01630563.2019.1639728.

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22

Diop, Mamadou A., and María J. Garrido-Atienza. "Retarded evolution systems driven by fractional Brownian motion with Hurst parameter." Nonlinear Analysis: Theory, Methods & Applications 97 (March 2014): 15–29. http://dx.doi.org/10.1016/j.na.2013.11.008.

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23

Gil-Alana, Luis Alberiko, and Carlos Poza. "Seasonal Long Memory in Retail Sales in the G7 Countries." Fractal and Fractional 8, no. 11 (2024): 650. http://dx.doi.org/10.3390/fractalfract8110650.

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This article examines the seasonal patterns of retail sales in the G7 nations, a key component of private consumption. Using seasonal fractional integration, we assess whether shocks present a lasting or temporary effect on retail sales trends, considering the high seasonal component. We observe mean reversion in France, Germany, Italy, Japan, and the UK, and permanent effects in the cases of Canada and USA. However, these outcomes vary based on the error term model applied. These results offer valuable information for policymakers seeking to boost consumption depending on the seasonal long me
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24

Lapinski, R., N. Perico, A. Remuzzi, F. Sangalli, A. Benigni, and G. Remuzzi. "Angiotensin II modulates glomerular capillary permselectivity in rat isolated perfused kidney." Journal of the American Society of Nephrology 7, no. 5 (1996): 653–60. http://dx.doi.org/10.1681/asn.v75653.

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Studies in experimental animals and humans have documented that inhibition of the renin-angiotensin system by angiotensin-converting enzyme inhibitors reduces urinary protein excretion rate and retards the development of renal injury. Here we sought to investigate whether angiotensin II (All) modified the size-selective properties to macromolecules of the glomerular capillary barrier in isolated perfused rat kidney preparation. Compared with basal values, continuous All infusion into the renal artery at the rate of 3 or 8 ng/min, but not at 0.6 ng/min, induced a progressive and significant inc
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25

Lin, Yuanhua, Shanhe Wu, and Wu-Sheng Wang. "A Nonlinear Weakly Singular Retarded Henry-Gronwall Type Integral Inequality and Its Application." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/218507.

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We establish a class of new nonlinear retarded weakly singular integral inequality. Under several practical assumptions, the inequality is solved by adopting novel analysis techniques, and explicit bounds for the unknown functions are given clearly. An application of our result to the fractional differential equations with delay is shown at the end of the paper.
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26

Wadhwani, Meena, and Shubha Jain. "Kinetics of Photochemical Oxidation of Glucose by Chloramine-T in Acidic Medium: A Mechanistic Approach." Advanced Materials Research 816-817 (September 2013): 7–12. http://dx.doi.org/10.4028/www.scientific.net/amr.816-817.7.

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A simple, convenient and accurate method for the kinetic study of photochemical oxidation of glucose by chloramine-T in acidic medium is described. The kinetic investigation shows the first order dependence of reaction rate on chloramine-T. With excess concentration of other reactants the reaction rate follows fractional order kinetics with respect to substrate. The reaction is catalyzed by H+ ions as well. A small salt effect and increase in reaction rate with increasing the intensity of light source is also observed. Addition of p-toluene sulphonamide retards the reaction rate. A suitable me
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27

M., ZAMEELA, BHASKARA SASTRY C., and S. A. DIKSHITULU L. "Kinetics and Mechanism of Ruthenium(Ill)-catalysed Oxidation of Selenium(IV) by Manganese(III)." Journal of Indian Chemical Society Vol. 75, Feb 1998 (1998): 63–66. https://doi.org/10.5281/zenodo.5913341.

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Department of Inorganic and Analytical Chemistry, School of Chemistry, Andhra University, Visakhapatnam-530 003 <em>Manuscript received 19 May 1995, revised 5 August 1996, accepted 14 February 1997</em> The title reaction is first order each in oxidant and catalyst and retarded by Mn<sup>II</sup>. The order in Se<sup>IV</sup> is unity at lower concentrations and fractional at higher concentrations. Increase in [<strong>H<sup>+</sup></strong>] retards the rate of the reaction but variation in ionic strength has negligible effect. A suitable mechanism involving Ru<sup>VIII</sup> as active oxidis
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28

Vanangamudi, G., and S. Srinivasan. "Kinetic Studies on the Oxidation of Someparaandmeta-Substituted Cinnamic Acids by Pyridinium Bromochromate in the Presence of Oxalic Acid (A Co-oxidation Study)." E-Journal of Chemistry 6, no. 3 (2009): 920–27. http://dx.doi.org/10.1155/2009/242743.

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The kinetics of oxidation of cinnamic acids by pyridinium bromochromate (PBC) in the presence of oxalic acid has been studied in acetic acid-water (60:40%) medium. The reaction shows unit order dependence each with respect to oxidant as well as oxalic acid [OX], the order with respect to [H+] and [CA] are fractional. The reaction is acid catalyzed and a low dielectric constant favours the reaction. Increase the ionic strength has no effect on the reaction rate. In the case of substituted cinnamic acids the order with respect to substrate vary depending upon the nature of the substituent presen
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29

Abu Falahah, Ibraheem, Amel Hioual, Mowafaq Omar Al-Qadri, et al. "Synchronization of Fractional Partial Difference Equations via Linear Methods." Axioms 12, no. 8 (2023): 728. http://dx.doi.org/10.3390/axioms12080728.

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Discrete fractional models with reaction-diffusion have gained significance in the scientific field in recent years, not only due to the need for numerical simulation but also due to the stated biological processes. In this paper, we investigate the problem of synchronization-control in a fractional discrete nonlinear bacterial culture reaction-diffusion model using the Caputo h-difference operator and a second-order central difference scheme and an L1 finite difference scheme after deriving the discrete fractional version of the well-known Degn–Harrison system and Lengyel–Epstein system. Usin
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30

Huang, Tingsheng, Chunyang Wang, and Xuelian Liu. "Depth Image Denoising Algorithm Based on Fractional Calculus." Electronics 11, no. 12 (2022): 1910. http://dx.doi.org/10.3390/electronics11121910.

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Depth images are often accompanied by unavoidable and unpredictable noise. Depth image denoising algorithms mainly attempt to fill hole data and optimise edges. In this paper, we study in detail the problem of effectively filtering the data of depth images under noise interference. The classical filtering algorithm tends to blur edge and texture information, whereas the fractional integral operator can retain more edge and texture information. In this paper, the Grünwald–Letnikov-type fractional integral denoising operator is introduced into the depth image denoising process, and the convoluti
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31

Mazhgikhova, M. G. "Dirichlet Problem for a Fractional-Order Ordinary Differential Equation with Retarded Argument." Differential Equations 54, no. 2 (2018): 185–92. http://dx.doi.org/10.1134/s0012266118020052.

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32

Arunsawatwong, Suchin, and Quang Van Nguyen. "Design of retarded fractional delay differential systems using the method of inequalities." International Journal of Automation and Computing 6, no. 1 (2009): 22–28. http://dx.doi.org/10.1007/s11633-009-0022-x.

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33

Gil-Alana, Luis A., and James E. Payne. "Time series dynamics of US retail gasoline prices: Evidence from fractional integration." Energy Sources, Part B: Economics, Planning, and Policy 12, no. 12 (2017): 1066–73. http://dx.doi.org/10.1080/15567249.2017.1360965.

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34

Kapalka, Brian A., Kaan Katircioglu, and Martin L. Puterman. "RETAIL INVENTORY CONTROL WITH LOST SALES, SERVICE CONSTRAINTS, AND FRACTIONAL LEAD TIMES." Production and Operations Management 8, no. 4 (2009): 393–408. http://dx.doi.org/10.1111/j.1937-5956.1999.tb00315.x.

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35

CA, Pranav D. Mandke CFA, and Eknath B. Khedkar Dr. "Financial Literacy and Its Impact on The Adoption of Fintech Solutions: A Study of Fractional Shares and Retail Investor Behaviour." International Journal of Advance and Applied Research S6, no. 22 (2025): 454–62. https://doi.org/10.5281/zenodo.15502073.

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<em>Fintech advancements like fractional shares have opened doors that were up until now, incomprehensible to ordinary Investors and has democratized the capital markets. However, the success of these fintech products will be determined by customers' financial literacy. The adoption of fractional shares by retail investors and their financial literacy are the subjects of this study. We had the option to get both subjective and quantitative information from our experiences by utilizing blended strategies. Our examination shows that increased financial literacy works on financial comprehension;
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36

Ruiz-Real, José, Juan Uribe-Toril, Juan Gázquez-Abad, and Jaime de Pablo Valenciano. "Sustainability and Retail: Analysis of Global Research." Sustainability 11, no. 1 (2018): 14. http://dx.doi.org/10.3390/su11010014.

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In recent years, the topic of sustainability has gained prominence in many retail sectors. Sustainability is a key element for retailers, who have seen that sustainable development could become an important source of competitive advantage. The purpose of this work is to highlight state of the art sustainability in retailing, for which a bibliometric analysis has been carried out using Web of Science online and Scopus database. Our findings show the most influential countries, journals, authors, and areas of knowledge interested in the topic. By using a fractional counting method to analyze co-
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37

Bhagwat, V. W., J. Tiwari, A. Choube, and B. Pare. "Kinetics and mechanism of cetyltrimethylammonium bromide catalyzed oxidation of diethylene glycol by chloramine-T in acidic medium." Journal of the Serbian Chemical Society 68, no. 7 (2003): 535–42. http://dx.doi.org/10.2298/jsc0307535b.

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The kinetics and mechanism of the C16TABcatalyzed oxidation of diethylene glycol (2,2?-oxydiethanol) by chloramine-T in acidic medium has been studied. The reaction has a first-order dependence on chloramine-T. With excess concentrations of other reactants, the reaction rate follows fractional order kinetics with respect to [diethylene glycol]. The micellar effect due to cetyltrimethylammonium bromide, a cationic surfactant, has been studied. The reaction is catalyzed by chloride ions as well. The small salt effect and increase in the reaction rate with increasing dielectric constant suggest t
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38

Nathani, Dr. Riya, and Bhadra Aariya Bijon. ""The Role of Technology and Innovation in Democratizing Alternative Investments for Retail Investors"." International Journal of Research 12, no. 4 (2025): 559–68. https://doi.org/10.5281/zenodo.15328262.

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Alternative investments&mdash;such as private equity, venture capital, real estate, peer-to-peer lending, digital gold, and tokenised assets&mdash;have emerged as powerful tools for diversifying portfolios and achieving non-market-correlated returns. Historically, these assets were restricted to institutional or high-net-worth investors due to high capital thresholds, illiquidity, and regulatory complexity. However, the financial landscape is evolving. Technology-led platforms like Smallcase, GripInvest, Pyse, and RealX are increasingly enabling access to alternative investments through fracti
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39

Maleki, Mohammad, and Ali Davari. "Fractional retarded differential equations and their numerical solution via a multistep collocation method." Applied Numerical Mathematics 143 (September 2019): 203–22. http://dx.doi.org/10.1016/j.apnum.2019.04.009.

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40

Quintino, Derick David, and Paulo Ferreira. "Diesel prices in Brazil: A dynamic fractional integration analysis." Economics and Business Letters 10, no. 2 (2021): 116–25. http://dx.doi.org/10.17811/ebl.10.2.2021.116-125.

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We investigate the behaviour of retail diesel prices in Brazil using fractional integration, with weekly data from January 2010 to April 2020. In this period, we have 3 episodes of relevant economic implications in the country under analysis: i) impeachment of the Brazilian President; ii) the lorry-drivers’ strike; iii) the rise of the global Covid-19 epidemic. We use a sliding windows approach to analyze price dynamics over time. The results suggest that, at the beginning of the sample, prices were non-stationary and non-mean reverting but over the time results changed in the different region
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41

Hou, Lijia, Yali Qin, Huan Zheng, Zemin Pan, Jicai Mei, and Yingtian Hu. "Hybrid High-Order and Fractional-Order Total Variation with Nonlocal Regularization for Compressive Sensing Image Reconstruction." Electronics 10, no. 2 (2021): 150. http://dx.doi.org/10.3390/electronics10020150.

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Total variation often yields staircase artifacts in the smooth region of the image reconstruction. This paper proposes a hybrid high-order and fractional-order total variation with nonlocal regularization algorithm. The nonlocal means regularization is introduced to describe image structural prior information. By selecting appropriate weights in the fractional-order and high-order total variation coefficients, the proposed algorithm makes the fractional-order and the high-order total variation complement each other on image reconstruction. It can solve the problem of non-smooth in smooth areas
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42

Lolić, Ivana, Petar Sorić, and Marija Logarušić. "A sectoral perspective on the persistence of economic sentiment: mere transitory effect or a long memory process?" Review of Keynesian Economics 11, no. 3 (2023): 328–49. http://dx.doi.org/10.4337/roke.2023.03.03.

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Opposing the mainstream view that economic sentiment conveys information of purely short-term relevance, we assess the long memory characteristics of confidence indicators derived from Business and Consumer Surveys (BCS). We utilize a battery of fractional integration tests on five sectoral BCS indicators in 28 European economies. Conforming to social learning theory, we find that the examined confidence indicators in all five sectors exhibit noteworthy persistence. This finding stays intact in various robustness checks: across countries and for different fractional integration test specificat
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43

Navneet, Singh, Jain Amit, and Kumar Singh Dinesh. "Gain and Bandwidth Enhanced Optimized Notch Loaded Microstrip Antenna for 5G Applications." International Journal of Innovative Technology and Exploring Engineering (IJITEE) 11, no. 2 (2021): 32–36. https://doi.org/10.35940/ijitee.B9651.1211221.

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In this paper, a rectangular patch antenna is presented loaded with T-shaped notch as well as having truncated corner for the enhancement of gain and bandwidth which is bring into play for mid band of 5G applications. With design frequency of 3 GHz, this prototyped design antenna having 50 &Omega; microstrip line feed for impedance matching and simulation has been performed using IE3D Mentor Graphics simulation software. Fractional impedance 51.3% has been observed from 2.39 to 4.04 GHz. An enhanced peak gain of 5.05 dBi and maximum directivity of 6.214 dBi has been observed at 4.22 GHz and 4.
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44

Forbes, Michael S., Barbara A. Thornhill, Jordan J. Minor, Katherine A. Gordon, Carolina I. Galarreta, and Robert L. Chevalier. "Fight-or-flight: murine unilateral ureteral obstruction causes extensive proximal tubular degeneration, collecting duct dilatation, and minimal fibrosis." American Journal of Physiology-Renal Physiology 303, no. 1 (2012): F120—F129. http://dx.doi.org/10.1152/ajprenal.00110.2012.

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Unilateral ureteral obstruction (UUO) is the most widely used animal model of progressive renal disease. Although renal interstitial fibrosis is commonly used as an end point, recent studies reveal that obstructive injury to the glomerulotubular junction leads to the formation of atubular glomeruli. To quantitate the effects of UUO on the remainder of the nephron, renal tubular and interstitial responses were characterized in mice 7 and 14 days after UUO or sham operation under anesthesia. Fractional proximal tubular mass, cell proliferation, and cell death were measured by morphometry. Supero
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45

Dardinier, Thibault, Peter Müller, and Alexander J. Summers. "Fractional resources in unbounded separation logic." Proceedings of the ACM on Programming Languages 6, OOPSLA2 (2022): 1066–92. http://dx.doi.org/10.1145/3563326.

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Many separation logics support fractional permissions to distinguish between read and write access to a heap location, for instance, to allow concurrent reads while enforcing exclusive writes. Fractional permissions extend to composite assertions such as (co)inductive predicates and magic wands by allowing those to be multiplied by a fraction. Typical separation logic proofs require that this multiplication has three key properties: it needs to distribute over assertions, it should permit fractions to be factored out from assertions, and two fractions of the same assertion should be combinable
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Min, Liu. "Harnack Inequality and Applications for Stochastic Retarded Differential Equations Driven by Fractional Brownian Motion." Journal of Partial Differential Equations 30, no. 1 (2017): 84–94. http://dx.doi.org/10.4208/jpde.v30.n1.7.

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Benchohra, Mouffak, Mokhtar Boumaaza, and Cemil Tunç. "Erd\'elyi-Kober fractional differential inclusions in Banach space with retarded and advanced arguments." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 40, no. 1 (2020): 75. http://dx.doi.org/10.7151/dmdico.1218.

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Kumar, Pradeep, D. N. Pandey, and D. Bahuguna. "Approximations of solutions to a retarded type fractional differential equation with a deviated argument." Journal of Integral Equations and Applications 26, no. 2 (2014): 215–42. http://dx.doi.org/10.1216/jie-2014-26-2-215.

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Slama, Abdeldjalil, and Ahmed Boudaoui. "Approximate controllability of retarded impulsive stochastic integro-differential equations driven by fractional Brownian motion." Filomat 33, no. 1 (2019): 289–306. http://dx.doi.org/10.2298/fil1901289s.

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Akbari Moornani, Kamran, and Mohammad Haeri. "On robust stability of LTI fractional-order delay systems of retarded and neutral type." Automatica 46, no. 2 (2010): 362–68. http://dx.doi.org/10.1016/j.automatica.2009.11.006.

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