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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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. …”
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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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Backward Continuation of the Solutions of the Cauchy Problem for Linear Fractional System with Deviating Argument by Hristo Kiskinov, Mariyan Milev, Milena Petkova, Andrey Zahariev

“…Fractional calculus provides tools to model systems with memory effects; when coupled with delays, they model process histories inspired by two independent sources—the memory of the fractional derivative and the impact conditioned by the delays. …”
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New Forms of the Open Newton-Cotes-Type Inequalities for a Family of the Quantum Differentiable Convex Functions by Jarunee Soontharanon, Muhammad Ali, Shahram Rezapour, Muhammad Toseef, Thanin Sitthiwirattham

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Application of Multiobjective Optimization Based on Modified SPEA2 Method for Tuning FOPID plus Second-Order Derivative Controller in Hydraulic Turbine Governing System by Tian Tian, Qiang Huang, Jinhua Lv, Mo Zhou, Jian Tang

“…In addition, we develop a modified strength Pareto evolutionary algorithm II (MSPEA2) to optimize the design parameters with multiple objectives. By combining fractional calculus and second-order derivative, the FOPID2D controller offers enhanced control flexibility compared to conventional PID controller. …”
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Analysis of Fractional Thin Film Flow of Third Grade Fluid in Lifting and Drainage via Homotopy Perturbation Procedure by Mubashir Qayyum, Farnaz Ismail, Syed Inayat Ali Shah, Muhammad Sohail, Kanayo Kenneth Asogwa, Fatema Tuz Zohra

“…We have expanded the formulations of non-Newtonian third grade fluid for lifting and draining in fractional space. Fractional calculus along with Homotopy Perturbation Method is used for the solution and analysis purposes. …”
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Fractional-Order Modeling and Analysis of a Variable Structure Hybrid Energy Storage System for EVs by Jianlin Wang, Dan Xu, Jiahui Zhou, Jinlu Mao

“…Fortunately, the theory of fractional calculus can help build accurate mathematical models of hybrid energy storage systems. …”
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Explicit travelling wave solutions to the time fractional Phi-four equation and their applications in mathematical physics by Ayesha Farooq, Tooba Shafique, Muhammad Abbas, Asnake Birhanu, Y. S. Hamed

“…Abstract In applied research, fractional calculus plays an important role for comprehending a wide range of intricate physical phenomena. …”
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Phase-lag mixed integral equation of a generalized symmetric potential kernel and its physical meanings in (3+1) dimensions by Azhar Rashad Jan

“…By applying the properties of fractional calculus, it is possible to get an integro-differential Fredholm-Volterra integral equation (Io-DF-VIE). …”
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Applications of Riccati–Bernoulli and Bäcklund Methods to the Kuralay-II System in Nonlinear Sciences by Khudhayr A. Rashedi, Musawa Yahya Almusawa, Hassan Almusawa, Tariq S. Alshammari, Adel Almarashi

“…This work underscores the significance of fractional calculus in analyzing complex wave phenomena and provides a robust framework for further exploration in nonlinear sciences and optical wave modeling.…”
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Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image by Yi-Fei Pu, Ji-Liu Zhou, Patrick Siarry, Ni Zhang, Yi-Guang Liu

“…To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. …”
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Evaluating the stability and efficacy of fractal-fractional models in reproductive cancer apoptosis with ABT-737 by Kottakkaran Sooppy Nisar, M. Sivashankar, S. Sabarinathan, C. Ravichandran, V. Sivaramakrishnan

“…The numerical schemes utilize the basic concepts of fractional calculus and Lagrange polynomial interpolation. …”
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Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systems by Asfand Fahad, Zammad Ali, Shigeru Furuichi, Yuanheng Wang

“…On the other hand, fractional calculus has emerged as an indispensable tool in Engineering, Physics, and Mathematics, with widespread applications. …”
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Performances improvement of DC Motor using a Fractional Order Adaptive PID Controller optimized by Genetic Algorithm by Abdelouaheb Boukhalfa, Yassine Bensafia, Khatir Khettab

“… In the past 20 years, scientists and engineers have rediscovered fractional calculus and have begun using it in more and more domains, most notably control theory. …”
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A novel approach to Lyapunov stability of Caputo fractional dynamic equations on time scale using a new generalized derivative by Michael Precious Ineh, Edet Peter Akpan, Hossam A. Nabwey

“…The results presented in this work contributed to the broader understanding of fractional calculus on time scales, enriching the theoretical foundation of dynamic systems analysis. …”
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Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative by Ndolane Sene, Babacar Sène, Seydou Nourou Ndiaye, Awa Traoré

“…Recent studies in fractional calculus have included new fractional derivatives with exponential kernels and Mittag-Leffler kernels. …”
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Fractional Stress Relaxation Model of Rock Freeze-Thaw Damage by Q. Liu, W. Chen, J. K. Guo, R. F. Li, D. Ke, Y. Wu, W. Tian, X. Z. Li

“…To accurately describe the mechanical behaviour of stress relaxation of rocks under freeze-thaw, the software element is constructed based on the theory of fractional calculus to replace the ideal viscous element in the traditional element model. …”
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Research on Slope Deformation Prediction Based on Fractional-Order Calculus Gray Model by Li Li, Yue Qiang, Shaohong Li, Zhongchao Yang

“…The fractional-order gray model is compared with the traditional gray models; therefore, the results show that the accuracy of slope deformation prediction based on the gray coupling model of cumulative displacement and fractional calculus is significantly higher than that of the conventional gray model, and its error is in the acceptable range compared with the actual monitoring data, which can meet the needs of engineering application. …”
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Numerically pricing American and European options using a time fractional Black–Scholes model in financial decision-making by Omid Nikan, Jalil Rashidinia, Hossein Jafari

“…Reliable and efficient numerical techniques are essential for solving fractional differential models due to the global characteristics of fractional calculus. This paper focuses on the numerical solution for the TFBSE for American and European option pricing models by means of the local meshless radial basis function (RBF) interpolation. …”
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