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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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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On the Possibility of the Jerk Derivative in Electrical Circuits by J. F. Gómez-Aguilar, J. Rosales-García, R. F. Escobar-Jiménez, M. G. López-López, V. M. Alvarado-Martínez, V. H. Olivares-Peregrino

“…In this paper we show that the jerk dynamics are naturally obtained for electrical circuits using the fractional calculus approach with order γ. We consider fractional LC and RL electrical circuits with 1⩽γ<2 for different source terms. …”
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The g-generalized Mittag-Leffler (p,s,k)-function by Umbreen Ayub, Madiha Shafiq, Amir Abbas, Umair Khan, Anuar Ishak, Y.S. Hamed, Homan Emadifar

“…This paper introduces the generalization of ML function, hereafter referred to as the g-generalized ML (p,s,k)-function, which extends the applicability of fractional calculus and complex analysis to a broader range of problems. …”
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Qualitative financial modelling in fractal dimensions by Rami Ahmad El-Nabulsi, Waranont Anukool

“…The relationship between fractional calculus and fractals is well-known in the literature. …”
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Beyond Chaos in Fractional-Order Systems: Keen Insight in the Dynamic Effects by José Luis Echenausía-Monroy, Luis Alberto Quezada-Tellez, Hector Eduardo Gilardi-Velázquez, Omar Fernando Ruíz-Martínez, María del Carmen Heras-Sánchez, Jose E. Lozano-Rizk, José Ricardo Cuesta-García, Luis Alejandro Márquez-Martínez, Raúl Rivera-Rodríguez, Jonatan Pena Ramirez, Joaquín Álvarez

“…Fractional calculus (or arbitrary order calculus) refers to the integration and derivative operators of an order different than one and was developed in 1695. …”
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