An efficient collocation scheme for new type of variable-order fractional Lane–Emden equation by H. Azin, A. Habibirad, E. Hesameddini, M.H. Heydari

“…This paper involves the Vieta–Lucas (Vt-L) bases to solve types of variable-order (V-O) fractional Lane–Emden equation (linear and nonlinear). …”
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An Operational Matrix Technique for Solving Variable Order Fractional Differential-Integral Equation Based on the Second Kind of Chebyshev Polynomials by Jianping Liu, Xia Li, Limeng Wu

“…An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. …”
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An Operational Matrix Technique Based on Chebyshev Polynomials for Solving Mixed Volterra-Fredholm Delay Integro-Differential Equations of Variable-Order by Kamal R. Raslan, Khalid K. Ali, Emad M. H. Mohamed, Jihad A. Younis, Mohamed A. Abd El salam

“…In this work, an algorithm for finding numerical solutions of linear fractional delay-integro-differential equations (LFDIDEs) of variable-order (VO) is introduced. The operational matrices are used as discretization technique based on shifted Chebyshev polynomials (SCPs) of the first kind with the spectral collocation method. …”
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Modular quantum signal processing in many variables by Zane M. Rossi, Jack L. Ceroni, Isaac L. Chuang

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An Efficient Polynomial Chaos Method for Stiffness Analysis of Air Spring Considering Uncertainties by Feng Kong, Penghao Si, Shengwen Yin

“…To model the uncertainties in the air spring, the interval/random variables models are introduced. For response analysis of the interval/random variables models of the air spring system, a new unified orthogonal polynomial expansion method, named as sparse quadrature-based interval and random moment arbitrary polynomial chaos method (SQ-IRMAPC), is proposed. …”
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Investigation on Free Vibration of Rotating Cylindrical Shells with Variable Thickness by Liu Xiangdong, Hou Xiaoli, Bai Bin, Zeng Maolin

“…The scientific and effective method is to design the variable thickness of RCS (VTRCS) along the axial direction in response to this demand. …”
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An Innovative Online Adaptive High-Efficiency Controller for Micro Gas Turbine: Design and Simulation Validation by Rui Yang, Yongbao Liu, Xing He, Zhimeng Liu

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An Efficient Petrov–Galerkin Scheme for the Euler–Bernoulli Beam Equation via Second-Kind Chebyshev Polynomials by Youssri Hassan Youssri, Waleed Mohamed Abd-Elhameed, Amr Ahmed Elmasry, Ahmed Gamal Atta

“…Utilizing a suitable combination of second-kind Chebyshev polynomials as a basis in spatial variables, the proposed method elegantly and simultaneously satisfies pinned–pinned and clamped–clamped boundary conditions. …”
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An Eighth-Order Numerical Method for Spatial Variable-Coefficient Time-Fractional Convection–Diffusion–Reaction Equations by Yuelong Feng, Xindong Zhang, Leilei Wei

“…In this paper, we propose a high-order compact difference scheme for a class of time-fractional convection–diffusion–reaction equations (CDREs) with variable coefficients. Using the Lagrange polynomial interpolation formula for the time-fractional derivative and a compact finite difference approximation for the spatial derivative, we establish an unconditionally stable compact difference method. …”
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An adaptive sliding mode fault-tolerant control of variable speed reaching law for steer-by-wire systems by Jinwen Yang, Yinquan Yu, Dequan Zeng, Yiming Hu, Junhui Liu, Kai Liu, Giuseppe Carbone, Shaohua Luo, Xiaofeng Zhu

“…To solve the inadequate tracking accuracy resulting from actuator fault and system disturbances, an adaptive sliding mode fault-tolerant control strategy based on a variable-speed reaching law (VSRL-ASMFTC) is proposed. …”
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A Convergent Legendre Spectral Collocation Method for the Variable-Order Fractional-Functional Optimal Control Problems by Zahra Pirouzeh, Mohammad Hadi Noori Skandari, Kameleh Nassiri Pirbazari

“…In addition, the matrix differentiation is calculated accurately and efficiently, overcoming the difficulties posed by variable-order fractional derivatives. …”
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Efficient Numerical Schemes for a Heterogeneous Reaction–Diffusion System with Applications by Samima Akhter, Md. Ariful Islam Arif, Rubayyi T. Alqahtani, Samir Kumar Bhowmik

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High-Order Spectral Method of Density Estimation for Stochastic Differential Equation Driven by Multivariate Gaussian Random Variables by Hongling Xie

“…There are some previous works on designing efficient and high-order numerical methods of density estimation for stochastic partial differential equation (SPDE) driven by multivariate Gaussian random variables. …”
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Advanced hybrid intelligence evaluation of nanomedicine delivery to various organs using machine learning and adaptive tree structured Parzen estimator by Wael A. Mahdi, Adel Alhowyan, Ahmad J. Obaidullah

“…Abstract We have examined the efficiency of drug delivery for targeted therapy by theoretical models. …”
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A Penalized Orthogonal Kriging Method for Selecting a Global Trend by Xituo Zhang, Guoxing Gao, Jianxin Zhao, Xinmin Li

“…In this paper, we introduce a new method for combining orthogonal kriging with penalized variable selection. Furthermore, an efficient algorithm is given to select the correct mean function. …”
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Prediction of Maximum Precipitation in Turkey with Polynomial Regression by Fatih Dikbaş, Orhan Koç

“…Understanding the expected variability in precipitation events and predicting the location and yearly periods of probable extreme precipitation are important for the efficient prevention of potential natural catastrophes like floods and dam failures. …”
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Efficient Probabilistic Evaluation and Sensitivity Analysis of Load Supply Capability for Renewable-Energy-Based Power Systems by Jie Zhang, Kaixiang Fu, Weizhi Huang, Yilin Zhang, Qing Sun, Yuan Chi, Junjie Tang

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Polynomial Chaos Expansion Approach to Interest Rate Models by Luca Di Persio, Gregorio Pellegrini, Michele Bonollo

“…The Polynomial Chaos Expansion (PCE) technique allows us to recover a finite second-order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochastic quantity ξ, hence acting as a kind of random basis. …”
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Polynomial and Differential Networks for End-to-End Autonomous Driving by Youngseong Cho, Kyoungil Lim

“…This study introduces a novel model for predicting control variables in end-to-end autonomous driving by leveraging polynomial and differential networks. …”
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A Numerical Scheme Based on the Chebyshev Functions to Find Approximate Solutions of the Coupled Nonlinear Sine-Gordon Equations with Fractional Variable Orders by MohammadHossein Derakhshan

“…To solve the problem, first, we obtain the operational matrix of the Caputo-Prabhakar fractional derivative of shifted Chebyshev polynomials. Then, this matrix and collocation method are used to reduce the solution of the nonlinear coupled variable-order fractional sine-Gordon equations to a system of algebraic equations which is technically simpler for handling. …”
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