ABC Fractional Derivative for Varicella-Zoster Virus Using Two-Scale Fractal Dimension Approach with Vaccination by Jirong Yang, Farkhanda Afzal, Perpetual Appiah

“…At the end, we provide the graphical results showing the effectiveness of two-scale dimension and fractional calculus in the current model.…”
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The Hermite–Hadamard–Mercer Type Inequalities via Generalized Proportional Fractional Integral Concerning Another Function by Tariq A. Aljaaidi, Deepak B. Pachpatte

“…In order to be able to study cosmic phenomena more accurately and broadly, it was necessary to expand the concept of calculus. In this study, we aim to introduce a new fractional Hermite–Hadamard–Mercer’s inequality and its fractional integral type inequalities. …”
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Applications of Some Generalized Janowski Meromorphic Multivalent Functions by Bakhtiar Ahmad, Muhammad Ghaffar Khan, Maslina Darus, Wali Khan Mashwani, Muhammad Arif

“…In this article, the ideas of post-quantum calculus and meromorphic multivalent functions are combined and some applications of these functions are discussed. …”
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Bounds for the Jensen Gap in terms of Power Means with Applications by Xuexiao You, Muhammad Adil Khan, Hamid Reza Moradi

“…Related results have been given in quantum calculus. As consequences, improvements of quantum integral version of Hermite-Hadamard inequality have been derived. …”
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Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity by Pawel Blasiak, Gérard H. E. Duchamp, Karol A. Penson

“…The paper is meant for nonspecialists as a gentle introduction to the field of graphical calculus and its applications in computational problems.…”
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Convexity of Certain q-Integral Operators of p-Valent Functions by K. A. Selvakumaran, S. D. Purohit, Aydin Secer, Mustafa Bayram

“…By applying the concept (and theory) of fractional q-calculus, we first define and introduce two new q-integral operators for certain analytic functions defined in the unit disc 𝒰. …”
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Fractional Dynamics of Genetic Algorithms Using Hexagonal Space Tessellation by J. A. Tenreiro Machado

“…Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions.…”
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Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control by Fathalla A. Rihan, Chinnathambi Rajivganthi, Palanisamy Muthukumar

“…We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. …”
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Computations of the M-Polynomials and Degree-Based Topological Indices for Dendrimers and Polyomino Chains by Young Chel Kwun, Adeel Farooq, Waqas Nazeer, Zohaib Zahid, Saba Noreen, Shin Min Kang

“…Moreover, by applying calculus, we compute nine important topological indices of under-study dendrimers and chains.…”
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The formal Laplace-Borel transform of Fliess operators and the composition product by Yaqin Li, W. Steven Gray

“…This gives a compact interpretation of the operational calculus of Fliess for computing the output response of an analytic nonlinear system.…”
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Anti-Periodic Dynamics of Quaternion-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays on Time Scales by Shiping Shen, Bing Li, Yongkun Li

“…Based on inequality analysis techniques on time scales, a fixed point theorem and the theory of calculus on time scales, the existence, and global exponential stability of anti-periodic solutions for this class of neural networks are established. …”
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Local Fractional Poisson and Laplace Equations with Applications to Electrostatics in Fractal Domain by Yang-Yang Li, Yang Zhao, Gong-Nan Xie, Dumitru Baleanu, Xiao-Jun Yang, Kai Zhao

“…From the local fractional calculus viewpoint, Poisson and Laplace equations were presented in this paper. …”
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Common Fixed Point Theorems on S-Metric Spaces for Integral Type Contractions Involving Rational Terms and Application to Fractional Integral Equation by G. S. Saluja, Hemant Kumar Nashine, Reena Jain, Rabha W. Ibrahim, Hossam A. Nabwey

“…In addition, the abstract conclusions are supported by an application of the Riemann-Liouville calculus to a fractional integral problem and a supportive numerical example.…”
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Stabilization and Tracking Control of Inverted Pendulum Using Fractional Order PID Controllers by Sunil Kumar Mishra, Dinesh Chandra

“…This work focuses on the use of fractional calculus to design robust fractional-order PID (PIλDμ) controller for stabilization and tracking control of inverted pendulum (IP) system. …”
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On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h-Convex Functions by Xiaobin Wang, Muhammad Shoaib Saleem, Kiran Naseem Aslam, Xingxing Wu, Tong Zhou

“…The Caputo–Fabrizio fractional derivatives are one of the important notions of fractional calculus. The aim of this paper is to present some properties of Caputo–Fabrizio fractional integral operator in the setting of h-convex function. …”
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Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay by S. J. Sadati, D. Baleanu, A. Ranjbar, R. Ghaderi, T. Abdeljawad (Maraaba)

“…Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. …”
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A Systematic Review on the Advancement in the Study of Fuzzy Variational Problems by Mansi Verma, Chuei Yee Chen, Adem Kılıçman, Risman Mat Hasim

“…In this paper, we provide a systematic review to recap the history of variational principle in the calculus of variations and compare it with the existing techniques in the fuzzy setting. …”
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Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems by George Voutsadakis

“…In their investigations they provide a sound and concretely complete calculus for the meet-combination based on available sound and complete calculi for the component systems. …”
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A Continuous-Time Model for Valuing Foreign Exchange Options by James J. Kung

“…This paper makes use of stochastic calculus to develop a continuous-time model for valuing European options on foreign exchange (FX) when both domestic and foreign spot rates follow a generalized Wiener process. …”
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Promoting Healthy Relationship Development in Teens, Part II: Three Key Qualities to Foster Better Relationships by Victor W. Harris, Gilon Marts, Muthusami Kumaran

“…Getting married and staying married require a complicated calculus of factors that must come together to produce healthy and satisfying relationships. …”
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