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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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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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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Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations by Latif Ur Rahman, Muhammad Arshad, Sabri T. M. Thabet, Imed Kedim

“…Using one of our main results, we solve a FDE from a broad class of fractional calculus. Eventually, we support our main results with a numerical example. …”
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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 a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses by Hasanen A. Hammad, Manuel De la Sen

“…Our analysis relies on concepts from stochastic analysis, fractional calculus, FP theory, semigroup theory, and the theory of multivalued maps (MVMs). …”
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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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