Robust Position Control of PMSM Using Fractional-Order Sliding Mode Controller by Jiacai Huang, Hongsheng Li, YangQuan Chen, Qinghong Xu

“…In the existing SMC method, the sliding surface is usually designed based on the integer-order integration or differentiation of the state variables, while in this proposed robust FOSMC algorithm, the sliding surface is designed based on the fractional-order calculus of the state variables. In fact, the conventional SMC method can be seen as a special case of the proposed FOSMC method. …”
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Study of Magnetohydrodynamic Pulsatile Blood Flow through an Inclined Porous Cylindrical Tube with Generalized Time-Nonlocal Shear Stress by Nehad Ali Shah, A. Al-Zubaidi, S. Saleem

“…The effects of pulsatile pressure gradient in the presence of a transverse magnetic field on unsteady blood flow through an inclined tapered cylindrical tube of porous medium are discussed in this article. The fractional calculus technique is used to provide a mathematical model of blood flow with fractional derivatives. …”
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Surgical Periodontal Management of Peripheral Ossifying Fibroma: A Series of Three Cases by Karo Parsegian, Roger M. Arce, Nikola Angelov

“…The treatment consisted of the removal of supra- and subgingival calculus, followed by a flap surgery with excision of the entire lesion ensuring the inclusion of the periosteal bed. …”
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Fractional-Order Sliding Mode with Active Disturbance Rejection Control for UAVs by Zhikun Zhang, Hui Zhang

“…The controller combines a fractional-order calculus operator and active disturbance rejection controller (ADRC) techniques to enhance the dynamic performance and robustness of the system. …”
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New Estimates of q1q2-Ostrowski-Type Inequalities within a Class of n-Polynomial Prevexity of Functions by Humaira Kalsoom, Muhammad Idrees, Dumitru Baleanu, Yu-Ming Chu

“…Different features and properties of excitement for quantum calculus have been examined through a systematic way. …”
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The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model by Tahir Khan, Zi-Shan Qian, Roman Ullah, Basem Al Alwan, Gul Zaman, Qasem M. Al-Mdallal, Youssef El Khatib, Khaled Kheder

“…We formulate the model and then fractionalize it using the concept of fractional calculus. For the purpose of fractionalizing, we use the Caputo–Fabrizio operator. …”
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Research on the wealth management fees of defined contribution pensions during the pre-retirement stage by Zongqi Sun, Peng Yang, Ying Wang, Jing Lu

“…Then, the Hamilton-Jacobi-Bellman (HJB) equation was formulated through the dynamic programming approach, and both the optimal investment strategy and minimum loss function were determined using calculus methods. Finally, how important parameters affect the initial optimal investment strategy and minimum loss function was analyzed, their economic implications were explained, the rationality of the model was validated, and several recommendations for management were provided.…”
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Period-Doubling Bifurcation of Stochastic Fractional-Order Duffing System via Chebyshev Polynomial Approximation by Youming Lei, Yanyan Wang

“…Fractional-order calculus is more competent than integer-order one when modeling systems with properties of nonlocality and memory effect. …”
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Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data by Zhenghai Ai, Xiaoqin Shu, Zeshui Xu

“…The intuitionistic fuzzy calculus (IFC), based on the basic operational laws of intuitionistic fuzzy numbers (IFNs), has been put forward. …”
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Congenital urethral diverticulum with a large stone in a 16-year-old male: a case report by Hazem Arab, Yousef Alsaffaf, Ahmed Aldolly, Mohammad Shehadeh

“…Conclusion This case illustrated the uncommon presentation of congenital Urethral diverticulum with a large calculus. The cause of congenital urethral diverticula is unknown, with multiple theories proposed. …”
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Optimal Insurance Indemnity for the Insured with Low Risk Tolerance by Jiesong Zhang, Cailing Li

“…To overcome this challenge, we apply the calculus of variations method employing a variable upper limit that is related to the maximal risk level. …”
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Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations by Qingxue Huang, Fuqiang Zhao, Jiaquan Xie, Lifeng Ma, Jianmei Wang, Yugui Li

“…The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. Also the fractional differential operational matrix is driven. …”
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Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context by Yousuf Alkhezi, Ahmad Shafee

“…Furthermore, this study examines the role of the Caputo operator in fractional calculus, offering insights into its significance in modeling real-world systems within the algebraic context. …”
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Chimera State in the Network of Fractional-Order FitzHugh–Nagumo Neurons by Janarthanan Ramadoss, Sajedeh Aghababaei, Fatemeh Parastesh, Karthikeyan Rajagopal, Sajad Jafari, Iqtadar Hussain

“…The fractional calculus in the neuronal models provides the memory properties. …”
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Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications by Thabet Abdeljawad, Qasem M. Al-Mdallal, Mohamed A. Hajji

“…Illustrative examples are discussed and an application about Sturm-Liouville eigenvalue problem in the sense of this new fractional difference calculus is given.…”
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Metabolic Changes after Urinary Diversion by Frank Van der Aa, Steven Joniau, Marcel Van Den Branden, Hein Van Poppel

“…Many patients are also subject to urinary calculus formation, both at the level of the upper urinary tract as in intestinal reservoirs. …”
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Urinothorax Caused by Xanthogranulomatous Pyelonephritis by Waiel Abusnina, Hazim Bukamur, Zeynep Koc, Fauzi Najar, Nancy Munn, Fuad Zeid

“…Its pathogenesis generally involves calculus obstructive uropathy and its histopathology is characterized by replacement of the renal parenchyma with lipid filled macrophages. …”
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Modeling Drug Concentration Level in Blood Using Fractional Differential Equation Based on Psi-Caputo Derivative by Muath Awadalla, Yves Yannick Yameni Noupoue, Kinda Abu Asbeh, Noureddine Ghiloufi

“…Theories and applications of fractional calculus are the main tools through which we establish main results. …”
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Foundational aspects of a new matrix holomorphic structure by Hedi Khedhiri, Taher Mkademi

“…Findings – We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties. Originality/value – We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. …”
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A Case of Drastic Reduction of Membranous Substances in the Pharynx by Interprofessional Cooperative Oral Care by Masahiko Okubo, Hideyuki Kamimura, Tsuyoshi Sato, Shoichiro Kokabu

“…There was a large amount of oral desquamated epithelium, dental plaque, and calculus in his mouth. Nurses and care workers administered oral care such as rubbing the tongue and buccal mucosa daily. …”
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