Fractal Control and Synchronization of the Discrete Fractional SIRS Model by Miao Ouyang, Yongping Zhang, Jian Liu

“…The discrete SIRS models with the Caputo deltas sense and the theories of fractional calculus and fractal theory provide a reasonable and sensible perspective of studying infectious disease phenomenon. …”
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Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable by Najla M. Alarifi, Rabha W. Ibrahim

“…We aim to generalize this class of equations using fractional calculus of a complex variable. We deal with a fractional integral operator type Prabhakar operator in the open unit disk. …”
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Existence of Mild Solutions for Fuzzy Fractional Evolution Equations via Krasnosel’skii Fixed Point Theorem by Ismail Airou, Ali El Mfadel, Elomari Mhamed

“…The proofs are based on fuzzy strongly continuous semigroups, a new Krasnoselskii fixed point theorem appropriate for fuzzy metric spaces, and some elementary fuzzy fractional calculus tools.…”
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Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations by Jan Čermák, Tomáš Kisela, Luděk Nechvátal

“…This paper investigates some initial value problems in discrete fractional calculus. We introduce a linear difference equation of fractional order along with suitable initial conditions of fractional type and prove the existence and uniqueness of the solution. …”
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Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System by Muhammad Marwan, Gauhar Ali, Ramla Khan

“…This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional-order gyrostat model with the help of a fixed-point theorem. …”
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Synchronization for a Class of Fractional-Order Hyperchaotic System and Its Application by Wen Tan, Feng Ling Jiang, Chuang Xia Huang, Lan Zhou

“…A new controller design method is proposed to synchronize the fractional-order hyperchaotic system through the stability theory of fractional calculus; the synchronization between two identical fractional-order Chen hyperchaotic systems is realized by designing only two suitable controllers in the response system. …”
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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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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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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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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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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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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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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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