Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System by Xianchen Wang, Zhen Wang, Shihong Dang

“…Combining fractional-order calculus theory and the Adomian algorithm, the dynamic phenomena of the incommensurate system caused by different fractional orders are studied. …”
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Consensus Tracking of Fractional-Order Multiagent Systems via Fractional-Order Iterative Learning Control by Shuaishuai Lv, Mian Pan, Xungen Li, Qi Ma, Tianyi Lan, Bingqiang Li, Wenyu Cai

“…The convergence conditions are proved using graph theory, fractional calculus, and λ norm theory. The theoretical analysis shows that the output of each agent completely tracks the expected trajectory in a limited time as the iteration number increases for both PDα-type and Dα-type FOILC algorithms. …”
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Flatness-based control revisited: The HEOL setting by Join, Cédric, Delaleau, Emmanuel, Fliess, Michel

“…The algebraic manipulations associated with the operational calculus lead to homeostat and intelligent controllers. …”
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Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar by M.-C. Casabán, J.-C. Cortés, B. García-Mora, L. Jódar

“…Random operational mean square calculus is developed for the introduced transforms. …”
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Some fractional integral inequalities involving extended Mittag-Leffler function with applications by Sabir Hussain, Rida Khaliq, Sobia Rafeeq, Azhar Ali, Jongsuk Ro

“…Integral inequalities and the Mittag-Leffler function play a crucial role in many branches of mathematics and applications, including fractional calculus, mathematical physics, and engineering. In this paper, we introduced an extended generalized Mittag-Leffler function that involved several well-known Mittag-Leffler functions as a special case. …”
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Routh–Hurwitz Stability and Quasiperiodic Attractors in a Fractional-Order Model for Awareness Programs: Applications to COVID-19 Pandemic by Taher S. Hassan, E. M. Elabbasy, A.E. Matouk, Rabie A. Ramadan, Alanazi T. Abdulrahman, Ismoil Odinaev

“…In conclusion, the findings indicate the effectiveness of fractional-order calculus to simulate, predict, and control the spread of epidemiological diseases.…”
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Spontaneous ureteral rupture: A rare case report and review of literature by Anass El Alaoui, MD, Abdelghani Ouraghi, MD, Hemdellah Debbe Salem, MD, Anouar El Moudane, MD, Ali Barki, MD

“…This case demonstrates that spontaneous ureteral rupture should be suspected in urolothiasis patients presenting for a severe pain even if the calculus is small and the laboratory markers are normal. …”
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Perspectives of Experts in the Selection of Contents for a Course of Differential Equations in Engineering by José Luis Díaz Palencia

“…Notably, experts highlighted variational calculus and energy representations as critical yet underrepresented areas in Differential Equations courses, essential for modeling complex, nonlinear problems. …”
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Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction by Ferial Ghaemi, Robiah Yunus, Ali Ahmadian, Soheil Salahshour, Mohamed Suleiman, Shanti Faridah Saleh

“…The fuzzy approximate solution is derived based on the Legendre polynomials to the fuzzy fractional equation calculus. Moreover, the complete error analysis is explained based on the application of fuzzy Caputo fractional derivative. …”
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Output Feedback Fractional-Order Nonsingular Terminal Sliding Mode Control of Underwater Remotely Operated Vehicles by Yaoyao Wang, Jiawang Chen, Linyi Gu

“…For the 4-DOF (degrees of freedom) trajectory tracking control problem of underwater remotely operated vehicles (ROVs) in the presence of model uncertainties and external disturbances, a novel output feedback fractional-order nonsingular terminal sliding mode control (FO-NTSMC) technique is introduced in light of the equivalent output injection sliding mode observer (SMO) and TSMC principle and fractional calculus technology. The equivalent output injection SMO is applied to reconstruct the full states in finite time. …”
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Periodontal Status in Smokers and Nonsmokers: A Clinical, Microbiological, and Histopathological Study by Maddipati Sreedevi, Alampalli Ramesh, Chini Dwarakanath

“…Both groups showed almost similar plaque levels (P=0.258), but smokers had reduced gingival (0.62 ± 0.31) and bleeding indices (28.53 ± 17.52) and an increased calculus index (1.62 ± 0.36). Smokers had an increased probing depth of 4–7 mm (P=0.009) and overall increased CAL. …”
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Molecular modelling of betalactamic antibiotic by Elso Manuel Cruz Cruz, Grettel Díaz Ramón

“…<strong><br />Method</strong>: The molecular structures were optimized with PM3• semiempiric calculus. The structure of the betalactamic ring in the different compounds was compared. …”
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Backstepping Sliding Mode Control Algorithm for Unmanned Aerial Vehicles Based on Fractional-Order Theory by Yanzhu Zhang, Bo Zhuang, Chunhao Ma, Cheng Zhang

“…This paper combines the fractional-order calculus theory with the backstepping sliding mode control algorithm, using the backstepping control to compensate for the nonlinearity of the system and the fractional-order theory to eliminate the jitter brought about by the sliding mode control, and proposes a new fractional-order backstepping sliding mode control strategy for the trajectory tracking control of the quadrotor UAV. …”
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Fuzzy Fractional-Order PID Control for PMSG Based Wind Energy Conversion System with Sparse Matrix Converter Topology by Waleed Khaled Abdulrazaq Abdulrazaq, Ahmet Mete Vural

“…The FFOPID controller is chosen to combine the salient features of the fractional-order calculus and fuzzy logic operations to enhance the dynamic response of classical PID controller with fixed gains. …”
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Multiplication of Negative Scenarios: the Approach Public Administrations Could Use at Drafting General Rules by Mirko Pečarič

“… This paper addresses problems that emerge when draft laws are created without due regard for the calculus of probability. Although the latter should be sine qua non for future legislation, legislators usually do not use it despite the legislation’s pro future orientation. …”
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Relato de uma extensão em tempos de isolamento social: Criação de um recurso educacional sobre matemática na pandemia de COVID-19 by Leila Thomazelli Thieghi, Fabio Luiz Sant'Anna Cuppo

“…Keywords: Educational Resource, Mathematics Education, Scientific Dissemination, Differential and Integral Calculus. …”
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Results on Solution Set in Certain Interval-Valued Controlled Models by Savin Treanţă, Omar Mutab Alsalami

“…The methodology used in this paper is a combination of techniques from the Lagrange–Hamilton theory, calculus of variations, and control theory. This study could be immediately improved by including an analysis of this class of optimization problems by using curvilinear integrals instead of multiple integrals. …”
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Periodontal Status and Risk Factors among Adults of Sebha City (Libya) by Syed Wali Peeran, A. J. A. Ranjith Singh, G. Alagamuthu, Syed Ali Peeran, P. G. Naveen Kumar

“…Majority, 52.65% were, detected with shallow pockets followed by 30.08% with calculus, 12.17% had deep pockets, 3.31% had bleeding, and only 1.33% were healthy. …”
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Viscoelastic hydrodynamics and holography by Jay Armas, Akash Jain

“…We reformulate classical elasticity effective field theory using surface calculus in which the Goldstone scalars naturally define the position of higher-dimensional crystal cores, covering both elastic and smectic crystal phases. …”
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Evidence for the Paleoethnobotany of the Neanderthal: A Review of the Literature by Gerhard P. Shipley, Kelly Kindscher

“…., starch, pollen, phytoliths, and seeds) in soil and dental calculus, dental and tool wear, coprolites, and genetics, for Neanderthal’s nutritional, medicinal, and ritual use of plants, which includes 61 different taxa from 26 different plant families found at 17 different archaeological sites. …”
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