A sustainable method for analyzing and studying the fractional-order panic spreading caused by the COVID-19 pandemic by Muhammad Farman, Evern Hincal, Parvaiz Ahmad Naik, Ali Hasan, Aceng Sambas, Kottakkaran Sooppy Nisar

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A Fractional Order Hepatitis C Mathematical Model with Mittag-Leffler Kernel by Hashim M. Alshehri, Aziz Khan

“…Our numerical results are based on the Lagrange polynomial interpolation. We observe that the model of fractional order has the same behavior of the solutions as the integer order existing model.…”
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Resplittable threshold multi-broker proxy re-encryption scheme from lattices by Ju-yan LI, Chun-guang MA, Qian ZHAO

“…Two different encryption schemes and Lagrange polynomial were used to construct a resplittable threshold multi-broker proxy re-encryption scheme on the lattice,namely the encryption in the ciphertext input and output side was different from the encryption in the re-encryption side which make the bound of noise was more relaxed.Threshold multi proxy not only ensure the safety of re-encryption key,but also ensure re-encryption scheme can still work even if the individual proxy could not provide normal services.The scheme is proven IND-UniRTPRE-CPA secure.…”
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Matrix Transformations and Disk of Convergence in Interpolation Processes by Chikkanna R. Selvaraj, Suguna Selvaraj

“…Walsh proved that the difference of the Lagrange polynomial interpolant of 𝑓(𝑧)∈𝐴𝜌 and the partial sum of the Taylor polynomial of 𝑓 converges to zero on a larger set than the domain of definition of 𝑓. …”
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A hierarchical access control scheme based on Lagrange interpolation for mobile agents by Tsung-Chih Hsiao, Zhen-Yu Wu, Tzer-Long Chen, Yu-Fang Chung, Tzer-Shyong Chen

“…This article proposes to use a function defined by Lagrange polynomial to compute decryption key. Each host will be given a decryption key to access the confidential document by inputting a secret key into an interpolation function which is generated from Lagrange interpolation. …”
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A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points by Mudasir Younis, Haroon Ahmad, Mahpeyker Ozturk, Deepak Singh

“…This article uses a fixed point method to connect with Chua’s attractor model, incorporating the Atangana–Baleanu derivative using a two-step Lagrange polynomial. We introduce novel fixed point theorems using some special contractions followed by graphical representations of the convergence behavior of the iterative process. …”
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Integrating the Finite Element Method with a Data-Driven Approach for Dam Displacement Prediction by Chenfei Shao, Chongshi Gu, Zhenzhu Meng, Yating Hu

“…Moreover, with a Lagrange polynomial interpolation, we can obtain the distribution field of elastic modulus, rather than gaining one value for the whole dam in previous studies. …”
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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. We generate simulated graphical representations of these models for a variety of fractional-order values. …”
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Stabilization by feedback control of a novel stochastic chaotic finance model with time-varying fractional derivatives by Seyfeddine Moualkia, Yang Liu, Jinde Cao

“…The numerical simulations are done based on the Euler–Maruyama method and with the help of Lagrange polynomial interpolation, enabling the authors to extract meaningful results from the model. …”
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Fractional-order PID feedback synthesis controller including some external influences on insulin and glucose monitoring by Kottakkaran Sooppy Nisar, Muhammad Farman, Khadija Jamil, Saba Jamil, Evren Hincal

“…Numerical simulations to explore which is done by solutions with a two-step Lagrange polynomial for generalized Mittag Leffler kernel showed that prolonged and severe hyperglycemia was caused by regular release of adrenaline into the blood at different fractional order values and fractal dimensions by changing initial values for normal and diabetes patients. …”
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A comparative study of Lagrange and Gregory forward interpolation techniques for estimating new student enrollment trends in the faculty of Tarbiyah at IAIN Kediri by Ahmad Syamsudin, M. Syamsul Ma'arif

“…This study explores the Lagrange polynomial and Newton Gregory Forward polynomial interpolation methods in estimating new student enrollment trends in several study programs at the Faculty of Tarbiyah, IAIN Kediri. …”
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Lagrange Multivariate Polynomial Interpolation: A Random Algorithmic Approach by A. Essanhaji, M. Errachid

“…In this work, we propose a random algorithm for computing several interpolating multivariate Lagrange polynomials, called RLMVPIA (Random Lagrange Multivariate Polynomial Interpolation Algorithm), for any finite interpolation set. …”
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A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer by Esam Y. Salah, Bhausaheb Sontakke, Ahmed A. Hamoud, Homan. Emadifar, Atul Kumar

“…The equilibrium points were also studied and discussed after stem cell therapy, and the approximate solutions for the given model were obtained using the Adam Bashford method, which depends on interpolation with Lagrange polynomials. Finally, the model was simulated using the Mathematica software, and through the figures, we found that the components of the model approach the equilibrium point, which indicates the stability of the model at the equilibrium point. …”
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Influence of Non-Structural Localized Inertia on Free Vibration Response of Thin-Walled Structures by Variable Kinematic Beam Formulations by Alfonso Pagani, Francesco Zangallo, Erasmo Carrera

“…According to CUF, kinematic fields can be formulated either as truncated Taylor-like expansion series of the generalized unknowns or by using only pure translational variables by locally discretizing the beam cross-section through Lagrange polynomials. The resulting theories were, respectively, referred to as TE (Taylor Expansion) and LE (Lagrange Expansion) in recent works. …”
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