Series Solution Method Used to Solve Linear Caputo Fractional Initial Value Problems with Variable Coefficients by Aghalaya S Vatsala, Govinda Pageni

“…Computing the solution of the linear Caputo fractional differential equation with variable coefficients cannot be obtained in closed form as in the integer-order case. …”
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The Dirichlet problem for elliptic equation with several singular coefficients by Tuhtasin G. Ergashev

“…Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the Dirichlet problem for an elliptic equation with several singular coefficients in explicit form. …”
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Two-point boundary value problem for a partial differential equation in spaces of periodic functions by V.S. Ilkiv, Z.M. Nytrebych, P.Y. Pukach, M.I. Vovk

“…We investigate the two-point in time boundary value problem for the partial differential equations of the second-order with one spatial variable and constant coefficients. The problem is considered in in the spaces of functions which Fourier coefficients are characterized by exponential behavior on the Cartesian product of the time interval and spatial domain $\mathbb{R}/2\pi\mathbb{Z}$. …”
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Inverse Scattering Integrability and Fractional Soliton Solutions of a Variable-Coefficient Fractional-Order KdV-Type Equation by Sheng Zhang, Hongwei Li, Bo Xu

“…However, the solved fNLEEs are all constant-coefficient models. In this study, we establish a fractional-order KdV (fKdV)-type equation with variable coefficients and show that the IST is capable of solving the variable-coefficient fKdV (vcfKdV)-type equation. …”
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Dissipation Scaling with a Variable <i>C_ϵ</i> Coefficient in the Stable Atmospheric Boundary Layer by Marta Wacławczyk, Jackson Nzotungishaka, Paweł Jędrejko, Joydeep Sarkar, Szymon P. Malinowski

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Analysis and assessment of the validity dough "theory of functions of the complex variable" by Lidiya A. Muratova

“…In article the analysis of quality of the "Theory of Functions of a Complex Variable" test is carried out. …”
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Interpolation of the Function of Two Variables with Large Gradients in the Boundary Layers by A.I. Zadorin

“…The problem of interpolation for the function of two variables with large gradients in the boundary layers is investigated. …”
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A radial variable for de Sitter two-point functions by Manuel Loparco, Jiaxin Qiao, Zimo Sun

“…We show that the two-point function of a free massive scalar in the Bunch-Davies vacuum has an exponentially convergent series expansion in this variable with positive coefficients only. …”
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Improvement of Multi-functional Air-conditioning Water Heaters by Wang Haifeng, Li Yuduo, Yuan Huihui, Sun Yajuan, Zhang Shoubing, Dong Shanshan

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Solitons, Lumps, Breathers, and Interaction Phenomena for a (2+1)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation by Tianwei Qiu, Zhen Wang, Xiangyu Yang, Guangmei Wei, Fangsen Cui

“…In this paper, soliton solutions, lump solutions, breather solutions, and lump-solitary wave solutions of a (2+1)-dimensional variable-coefficient extended shallow-water wave (vc-eSWW) equation are obtained based on its bilinear form. …”
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Significance of dissipative flow on a second-grade nanofluid with variable thermal properties on the stretching surface by Zia Ullah, Aamir Abbas Khan, Shalan Alkarni, Abhinav Kumar, N. Beemkumar, Tushar Aggarwal, Ashwin Jacob, Jajneswar Nanda, Feyisa Edosa Merga

“…Boundary conditions are used for the analysis of heat and mass transmission. Stream functions and similarity variables are utilized to reduce the complexity of the governed PDEs (partial differential equations) and altered into ODEs (ordinary differential equations). …”
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Approximation of an Optimal BV -Control Problem in the Coefficient for the p(x)-Laplace Equation by Ismail Aydin, Peter Kogut

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Application of physics-informed neural networks for two-phase flow model with variable diffusion and experimental validation by Daulet Kalesh, Timur Merembayev, Sagyn Omirbekov, Yerlan Amanbek

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An Ultrafast Image Simulation Technique with Spatially Variable Point-spread Functions by Zeyu Bai, Peng Jia, Jiameng Lv, Xiang Zhang, Wennan Xiang, Lin Nie

“…During real observations, images obtained by optical telescopes are affected by spatially variable point-spread functions (PSFs), a crucial effect requiring accurate simulation. …”
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Impact of CYP3A4 functional variability on ziprasidone metabolism by Qi Zhou, Qi Zhou, Yameng Wu, Zhize Ye, Zheyan Zhang, Kai Zheng, Jianchang Qian, Zhongxiang Xiao, Yang Lu

“…This study explored the functional variability of CYP3A4 in ziprasidone metabolism, focusing on drug interactions and genetic polymorphisms.MethodsThe metabolic inhibition and kinetic properties of ziprasidone were evaluated through in vitro experiments utilizing rat liver microsomes (RLM), human liver microsomes (HLM), and CYP3A4 baculosomes. …”
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Enhanced thermal performance of variable cross-section solar collectors: a case study in Santiniketan, India by Pranab Kanti Roy

“…Abstract We present analytical models for variable cross-section absorber plate solar collectors, where the thermal conductivity, overall heat loss coefficient, and incident solar heat flux are power-law functions of temperature. …”
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EVALUATION OF SUBSOIL MASSIF STABILITY TAKING INTO ACCOUNT THE IRREGULARITY OF CONSTITUENT ROCKS ON THE BASIS OF A RANDOM SIZE AND FUNCTION MODEL by M. O. Allaev

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VEGETATIVE PROVISION INDICATORS OF CARDIOVASCULAR SYSTEM AND PHYSICAL EFFICIENCY OF WOMEN ATHLET-SPRINTERS by M. V. Didenko, E. L. Mikhalyuk, S. N. Malakhova

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Arbitrary Random Variables and Wiman’s Inequality by Andriy Kuryliak, Oleh Skaskiv, Andriy Bandura

“…We study the class of random entire functions given by power series, in which the coefficients are formed as the product of an arbitrary sequence of complex numbers and two sequences of random variables. …”
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High-Order Spectral Method of Density Estimation for Stochastic Differential Equation Driven by Multivariate Gaussian Random Variables by Hongling Xie

“…All the presented stochastic equations are driven by bivariate Gaussian random variables. The efficiency is compared with the Monte-Carlo method based on the known random function.…”
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