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Analyzing coupled wave dynamics in elastic waveguides with height variations: Modeling and insights

Partial Differential Equations in applied mathematics 2025年 14卷

作者： Afzal, Muhammad Aziz, Taha Department of Mathematics and Natural Sciences Center for Applied Mathematics and Bioinformatics Gulf University for Science & Technology Hawally 32093 Kuwait Department of Mathematical Sciences DCC-KFUPM King Fahd University of Petroleum and Minerals (KFUPM) Dhahran 31261 Saudi Arabia Interdisciplinary Research Center for Sustainable Energy Systems (IRC-SES) KFUPM Dhahran 31261 Saudi Arabia

This study employs a combined mode matching technique and Galerkin approach to analyze fluid–structure coupled wave interactions a an elastic plate bounded waveguide containing height variation. The dynamical response of plate coupled with the acoustics govern higher order derivative involving boundary value problem. The associated eigenfunctions are non-orthogonal and the system underlies non-Sturm–Liouville system. The Galerkin approach is adopted to model the vibrational response of an elastic plate, while the continuity conditions at the fluid–structure interface are applied to get linear algebraic systems which are truncated and solved numerically. Results confirm power conservation, with reflected and transmitted powers summing to unity across all frequencies. For structure-borne modes, transmission dominates at lower frequencies but fluctuates near cut-on frequencies, while reflection dominates fluid-borne modes due to impedance mismatch. The model's accuracy is validated by adherence to power conservation and agreement with the tailored-Galerkin method, establishing a reliable framework for analyzing wave energy propagation in coupled systems. © 2025 The Authors

关键词： Flexible waveguide Fluid–structure coupling Galerkin approach Generalized orthogonality relation Mode-matching method

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Numerical solution of two dimensional time-fractional telegraph equation using Chebyshev spectral collocation method

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Partial Differential Equations in applied mathematics 2025年 13卷

作者： Kamran Ali Shah, Farman Shah, Kamal Abdeljawad, Thabet Department of Mathematics Islamia College Peshawar Peshawar Khyber Pakhtoonkhwa 25120 Pakistan Department of Mathematics and Sciences Prince Sultan University P.O. Box 66833 Riyadh 11586 Saudi Arabia Department of Mathematics Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Saveetha University Chennai Tamil Nadu 602105 India Center for Applied Mathematics and Bioinformatics (CAMB) Gulf University for Science and Technology Hawally 32093 Kuwait Department of Mathematics and Applied Mathematics School of Science and Technology Sefako Makgatho Health Sciences University Ga-Rankuwa South Africa

The 2D telegraph equation has numerous applications, such as signal processing, diffusion of biological species, and modeling wave propagation in electrical transmission lines. In this article, we present an efficient numerical scheme for solving the 2D time-fractional telegraph equation using a hybrid approach coupling the Laplace transform (LT) with the spectral collocation method based on Chebyshev nodes (ChSCM). The inclusion of the Caputo derivative in the classical telegraph equation provides a more accurate model for representing anomalous diffusion and wave propagation in heterogeneous media. The LT is employed to handle the time variable, transforming the considered equation into a system of spatial equations. These are then efficiently solved using the ChSCM. In the final step of our suggested approach, the numerical inversion of LT is performed to recover the solution in the time domain. This hybrid approach results in an efficient and robust numerical method. The convergence, accuracy, and stability of the method are verified using numerical examples. The acquired results show the potential of this numerical scheme for approximating the 2D time-fractional partial differential equations. © 2025 The Authors

关键词： Caputo derivative Laplace transform Modified Talbot's method Spectral method Telegraph equation

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Towards Invariance to Node Identifiers in Graph Neural Networks

arXiv

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arXiv 2025年

作者： Bechler-Speicher, Maya Eliasof, Moshe Schönlieb, Carola-Bibiane Gilad-Bachrach, Ran Globerson, Amir Blavatnik School of Computer Science Tel-Aviv University Meta United States Department of Applied Mathematics and Theoretical Physics University of Cambridge United Kingdom Department of Bio-Medical Engineering Tel-Aviv University Edmond J. Safra Center for Bioinformatics Tel-Aviv University Google Research United States

Message-Passing Graph Neural Networks (GNNs) are known to have limited expressive power, due to their message passing structure. One mechanism for circumventing this limitation is to add unique node identifiers (IDs), which break the symmetries that underlie the expressivity limitation. In this work, we highlight a key limitation of the ID framework, and propose an approach for addressing it. We begin by observing that the final output of the GNN should clearly not depend on the specific IDs used. We then show that in practice this does not hold, and thus the learned network does not possess this desired structural property. Such invariance to node IDs may be enforced in several ways, and we discuss their theoretical properties. We then propose a novel regularization method that effectively enforces ID invariance to the network. Extensive evaluations on both real-world and synthetic tasks demonstrate that our approach significantly improves ID invariance and, in turn, often boosts generalization performance. © 2025, CC BY.

关键词： Graph neural networks

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On some integral inequalities of Grüss type involving the generalized fractional Saigo k-integral operator

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Heliyon 2025年第2期11卷 e41702页

作者： Abbas, Akhtar Mubeen, Shahid Khan, Aziz Abdeljawad, Thabet Department of Mathematics University of Sargodha Sargodha 40162 Pakistan Department of Mathematics Baba Guru Nanak University Nankana Sahib Pakistan Department of Mathematics Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Saveetha University Tamil Nadu Chennai 602105 India Department of Mathematics and Science Prince Sultan University P.O. Box 66833 Riyadh 11586 Saudi Arabia Center for Applied Mathematics and Bioinformatics (CAMB) Gulf University for Science and Technology Hawally 32093 Kuwait Department of Medical Research China Medical University Taichung 40402 Taiwan Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University South Africa

Using the generalized Saigo fractional integral operator, the authors of this study prove several novel fractional integral inequalities of the Grüss type. By fixing the values of functions, specific situations derived from previously established findings are shown. The ultimate purpose of this work is to investigate the Grüss-type integral inequalities with the Saigo k-integral operator, a more generalized integral operator. We also elaborate on a few more outcomes and specific instances of the primary findings. © 2025 The Author(s)

关键词： Generalized hypergeometric function Grüss integral inequalities Saigo's k-fractional integral operator

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On generalized fractal-fractional derivative and integral operators associated with generalized Mittag-Leffler function

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Heliyon 2025年第4期11卷 e42144页

作者： Khan, Hira Rahman, Gauhar Samraiz, Muhammad Shah, Kamal Abdeljawad, Thabet Department of Mathematics and Statistics Hazara University Mansehra 21300 Pakistan Department of Mathematics University of Sargodha P.O. Box 40100 Sargodha Pakistan Department of Mathematics and Sciences Prince Sultan University Riyadh 11586 Saudi Arabia Department of Mathematics Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Saveetha University Tamil Nadu Chennai 602105 India Department of Medical Research China Medical University Taichung 40402 Taiwan Department of Mathematics and Applied Mathematics School of Science and Technology Sefako Makgatho Health Sciences University Ga-Rankuwa South Africa Center for Applied Mathematics and Bioinformatics (CAMB) Gulf University for Science and Technology Hawally 32093 Kuwait

In recent years, the Atangana-Baleanu (AB) fractal-fractional derivatives are widely used in many fields. In 2017, Atangana defined such operators by utilizing one parameter Mittag-Leffler function (M-L) function. Such operators have not yet been studied for three parameters M-L function. In this paper, we discuss further modifications of Caputo Fabrizio (CF), AB and generalized Hattaf fractal-fractional (GHF) operators. We used the modified three parameters M-L function to define the generalized fractal-fractional (GFF) differential and integral operators. We study an innovative class of new generalized weighted differential and integral operators. We define the generalized fractal-fractional (GFF) differential and integral operators with generalized Mittag-Leffler (M-L) kernels, which are used to simulate the complex dynamics of several natural and physical phenomena in a variety of scientific and engineering domains. There are a few established features of the newly defined operators. An example of an application for this new class of GFF integral is presented. Also, we discussed the graphical comparison of this new GFF operator with the existing GHF, AB and CF derivatives. Our case is the more general case compared with the existing fractal-fractional operators. We have presented some novel results for the new operators both analytically and graphically. Also, we discussed some special cases by giving specific value to the parameter θ. All the classical operators are restored by applying certain conditions on parameters. © 2025 The Authors

关键词： AB operators CF operators Fractal fractional derivatives Fractal fractional integrals Fractional derivative Fractional integral GHF operators Laplace transform Mittag-Leffler function

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Optical wave features and sensitivity analysis of a coupled fractional integrable system

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Results in Physics 2025年 68卷

作者： Muhammad, Jan Younas, Usman Almutairi, D.K. Khan, Aziz Abdeljawad, Thabet Department of Mathematics Shanghai University No. 99 Shangda Road Shanghai 200444 China Department of Mathematics College of Science Al-Zulfi Majmaah University Saudi Arabia Department of Mathematics and Sciences Prince Sultan University Riyadh Saudi Arabia Department of Mathematics Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Saveetha University Tamil Nadu Chennai 602105 India Department of Medical Research China Medical University Taichung 40402 Taiwan Center for Applied Mathematics and Bioinformatics (CAMB) Gulf University for Science and Technology Hawally 32093 Kuwait Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University Garankuwa Medusa 0204 South Africa

This paper explores optical wave features of a coupled fractional integrable Akbota equation. The study of the dynamical systems governing the propagation of soliton waves across transcontinental and transoceanic distances through optical fibers is among the most intriguing fields of research. The Akbota equation, is a basic tool for investigating nonlinear phenomena in optics, differential geometry of curves, and magnetism. The optical wave solutions are extracted in the forms of different solitary waves as well as periodic, hyperbolic exponential function solutions. The solutions are extracted using sophisticated methods, such as the multivariate generalized exponential rational integral function approach and Kumar-Malik method. Moreover, the sensitivity analysis of the studied model is also discussed. In addition, a variety of plots demonstrating the effect of fractional derivatives are provided to observe the physical behavior of the derived solutions by the assistance of the parameters. The outcomes obtained indicate that the implemented computational strategies are proficient, succinct, effective and they can be combined with representative computations to tackle more intricate phenomena. © 2024 The Authors

关键词： Akbota equation Fractional derivatives Generalized multivariate exponential rational integral function technique Kumar-Malik method Nonlinear phenomena Optical solitons

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Computational scheme for the numerical solution of fractional order pantograph delay-integro-differential equations via the Bernstein approach

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Partial Differential Equations in applied mathematics 2025年 14卷

作者： Aourir, E. Dastjerdi, H. Laeli Shah, Kamal Abdeljawad, Thabet Laboratory of Mathematical Engineering and Computer Science Faculty of Science Ibn Zohr University Morocco Department of Mathematics Education Farhangian University P.O. Box 14665-889 Tehran Iran Department of Mathematics and Sciences Prince Sultan University Riyadh 11586 Saudi Arabia Department of Mathematics Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Saveetha University Tamil Nadu Chennai 602105 India Department of Mathematics and Applied Mathematics School of Science and Technology Sefako Makgatho Health Sciences University Ga-Rankuwa South Africa Center for Applied Mathematics and Bioinformatics (CAMB) Gulf University for Science and Technology Hawally 32093 Kuwait

The main objective of this research is to provide an efficient computational algorithm for solving a class of fractional order pantograph delay-integro-differential equations. The Bernstein approximation technique is employed for approximating the solutions of such equations by taking into account the properties of Bernstein polynomials, which transform the original problem into a simplified linear system of algebraic equations. The formulation of the suggested scheme is carefully described, and its convergence performance is examined. Both existence and uniqueness theorems are provided to establish the theoretical reliability of the methodology. Additionally, an estimation of the error bounds is reported to evaluate the precision of the approximation. The reliability, stability and computational effectiveness of the algorithm developed are confirmed by a series of numerical experiments. A comparative analysis with other available methodologies and analytical solutions further highlights the practicality and robustness of the new technique, offering reduced computational and memory costs. © 2025 The Authors

关键词： Bernstein approximation Caputo derivative Error analysis Fractional pantograph delay integro-differential equations

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Advancements in integral inequalities of Ostrowski type via modified Atangana-Baleanu fractional integral operator

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Heliyon 2025年第1期11卷 e41525页

作者： Rahman, Gauhar Samraiz, Muhammad Shah, Kamal Abdeljawad, Thabet Elmasry, Yasser Department of Mathematics and Statistics Hazara University Mansehra 21300 Pakistan Department of Mathematics University of Sargodha P.O. Box 40100 Sargodha Pakistan Department of Mathematics and Sciences Prince Sultan University Riyadh 11586 Saudi Arabia Department of Mathematics Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Saveetha University Tamil Nadu Chennai 602105 India Department of Medical Research China Medical University Taichung 40402 Taiwan Department of Mathematics and Applied Mathematics School of Science and Technology Sefako Makgatho Health Sciences University Ga-Rankuwa South Africa Center for Applied Mathematics and Bioinformatics (CAMB) Gulf University for Science and Technology Hawally 32093 Kuwait Department of Mathematics College of Science King Khalid University P.O. Box 9004 Abha 61466 Saudi Arabia

Convexity and fractional integral operators are closely related due to their fascinating properties in the mathematical sciences. In this article, we first establish an identity for the modified Atangana-Baleanu (MAB) fractional integral operators. Using this identity, we then apply Jensen integral inequality, Young's inequality, power-mean inequality, and Hölder inequality to prove several new generalizations of Ostrowski type inequality for the convexity of |ℵ|. From the primary findings, we also deduced a few new special cases. The results of this investigation are expected to indicate new advances in the study of fractional integral inequalities. © 2024 The Author(s)

关键词： Convex function Fractional operators Power mean inequality Young inequality

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Existence of solutions of multi-order fractional differential equations

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Partial Differential Equations in applied mathematics 2025年 13卷

作者： Bouchelaghem, Faycal Boulares, Hamid Ardjouni, Abdelouaheb Jarad, Fahd Abdeljawad, Thabet Abdalla, Bahaaeldin Shah, Kamal High School of Management Sciences Annaba Annaba 23000 Algeria Laboratory of Analysis and Control of Differential Equations “ACED” Faculty MISM Department of Mathematics University of Guelma Guelma 24000 Algeria Department of Mathematics and Informatics Univ Souk Ahras P.O. Box 1553 Souk Ahras 41000 Algeria Department of Mathematics Cankaya University Etimesgut Ankara 06790 Türkiye Center for Applied Mathematics and Bioinformatics (CAMB) Gulf University for Science and Technology Hawally 32093 Kuwait Department of Mathematics and Sciences Prince Sultan University P.O. Box 66833 Riyadh 11586 Saudi Arabia Department of Mathematics Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Saveetha University Tamil Nadu Chennai 602105 India Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University Garankuwa Medusa 0204 South Africa

Recently, the field of fractional calculus has garnered significant attention due to its wide range of applications across various disciplines in science and engineering. Numerous results have been derived using tools from numerical functional analysis and fixed point theory to address a variety of problems in this area. This study employs the Banach Fixed Point Theorem (BFPT) to establish the existence and uniqueness of solutions for Riemann–Liouville fractional differential equations (RLFDEs) involving multiple orders. Sufficient conditions for the existence of solutions to the problem under consideration have been provided. Furthermore, an illustrative example is presented to validate the theoretical findings. © 2025

关键词： Banach fixed point theorems Existence Multi-order Riemann–Liouville fractional derivatives Uniqueness

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Correction to: Assessing the phytosanitary threats of two non-native crickets under temperature change

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Journal of Pest Science 2025年第2期98卷 1203-1204页

作者： Kulessa, Anna K. Cuthbert, Ross N. Soto, Ismael Balzani, Paride Toutain, Mathieu Kouba, Antonín Haubrock, Phillip J. Department of Freshwater Ecology in Landscape Planning University of Kassel Kassel Germany Faculty of Fisheries and Protection of Waters South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses University of South Bohemia in České Budějovice Vodňany Czech Republic Institute for Global Food Security School of Biological Sciences Queen’s University Belfast Belfast UK Rennes France CAMB Center for Applied Mathematics and Bioinformatics Gulf University for Science and Technology Mubarak Al-Abdullah Kuwait Department of River Ecology and Conservation Senckenberg Research Institute and Natural History Museum Frankfurt Germany

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