Existence of Solutions for Boundary Value Problem of a Caputo Fractional Difference Equation by Zhiping Liu, Shugui Kang, Huiqin Chen, Jianmin Guo, Yaqiong Cui, Caixia Guo

“…The proofs are based upon the theory of discrete fractional calculus. We also provide some examples to illustrate our main results.…”
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Culioli, Adamczewski et la linguistique anglaise by Ariel Laurencio Tacoronte

“…In his research on the analysis of languages, Culioli (1968, 1971) states that it is essential to build a system of representation with formal properties in order to be able to perform a calculus in linguistics. We will try here to identify the basis of Culioli’s theoretical formalization which allowed Adamczewski (1978) to construct his metaoperational grammar of English, a grammar consisting of principles later established by this author as universal, starting from the English be + ing structure. …”
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M-Polynomials and Degree-Based Topological Indices of the Molecule Copper(I) Oxide by Faryal Chaudhry, Iqra Shoukat, Deeba Afzal, Choonkil Park, Murat Cancan, Mohammad Reza Farahani

“…In this paper, we derived closed formulas for some well-known degree-based topological indices like first and second Zagreb indices, the modified Zagreb index, the symmetric division index, the harmonic index, the Randić index and inverse Randić index, and the augmented Zagreb index using calculus.…”
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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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Effect of Structural Parameter on Stiffness of Parallel Two-axis Straight Circular Flexible Hinge by Li Cheng, He Tao, Chen Guoyu, Wang Chuanli, Jiang Hao, Ji Chenguang

“…In order to deeply analyze the micro-displacement deformation performance of parallel two-axis straight circular flexure hinge，based on the assumption of small deformation of elastic beam，the bending theory of variable cross-section continuous beam and the principle of calculus superposition，the calculating formulas of angular deformation and angular stiffness are derived. …”
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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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Students’ Perceptions of PBL Usefulness by Babo Lurdes, Mendonça Jorge, Pinto Carla

“…This paper describes and analyses a teaching framework based on PBL followed in the Differential and Integral Calculus and Statistical Models courses in a Biomedical Engineering Bachelor, at the School of Engineering, Polytechnic of Porto. …”
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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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