Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article An Investigation of Discontinuities in Time-Dependent 2D and 3D Parabolic Partial Differential Equations Utilizing Collocation Methods: A Comparative Analysis of Complex Interface Problems(Springer Heidelberg, 2025) Faheem, Muhammad; Asif, Muhammad; Amin, Rohul; Haider, Nadeem; Jarad, FahdParabolic double interface problems have many applications in the fields such as materials science, fluid dynamics, and heat transfer. This paper presents a comparison of the Haar wavelet-based collocation method and two variants of radial basis function (RBF) method for solving 2D and 3D, linear as well as nonlinear, parabolic double interface problems. The two variants of RBF methods are the multiquadric RBF method and the integrated RBF method. For linear problems, the system of equations obtained from the integrated RBF method is solved using Moore-Penrose pseudoinverse. Error analysis is performed using L infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_\infty $$\end{document} norm error and root mean square error, and the findings are discussed in detail. The methods are compared based on their accuracy and efficiency in solving different benchmark problems. The results show that both the Haar wavelet collocation method and the integrated RBF method perform better than the conventional RBF method in terms of accuracy.Article Citation - WoS: 14Citation - Scopus: 19On the Discrete Sumudu Transform(Editura Acad Romane, 2012) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Bayram, Kamm; Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; Köse, Hasan; Ameen, Raad; MatematikIn this paper, we define the Sumudu transform on an arbitrary time scale. Starting from this definition we define the discrete Sumudu transform. We prove the initial and final value problems and study the basic properties of this transform. We also present the discrete Sumudu transform of some basic functions.Article Citation - WoS: 5Citation - Scopus: 4Robust Numerical Techniques for Modeling Telegraph Equations in Multi-Scale and Heterogeneous Environments(Springer Heidelberg, 2025) Asif, Muhammad; Bilal, Faisal; Haider, Nadeem; Jarad, FahdThe article presents an innovative concept called the hyperbolic telegraph interface model, which effectively integrates regular interfaces. This hybrid method leverages Haar wavelets in conjunction with the finite difference method to provide robust numerical solutions. It is expertly designed for both linear and nonlinear models, adeptly handling constant or variable coefficients across regular interfaces. At the heart of this technique is the approximation of spatial derivatives using truncated Haar series, while time derivatives are efficiently processed through the finite difference method. The methodology has been rigorously tested across a variety of linear and nonlinear models, demonstrating its effectiveness. In linear problems, the algebraic system is solved with precision using the Gauss elimination method. For nonlinear challenges, the Quasi-Newton linearization formula is applied to successfully eliminate non-linearity from the model. To evaluate the technique's performance, we analyze key metrics such as maximum absolute errors, root mean square errors, and computational convergence rates with varying numbers of collocation points. The proposed approach consistently outperforms existing methods, particularly in situations involving abrupt changes in the solution space or discontinuities between boundary and initial conditions, delivering stable solutions in these critical scenarios. The combination of strong theoretical foundations and computational stability, along with excellent convergence rates and comprehensive numerical studies, firmly validates the accuracy and versatility of this method, confirming its wide range of applications.Article Citation - WoS: 1Citation - Scopus: 1No-Regret and Low-Regret Control for a Weakly Coupled Abstract Hyperbolic System(Wiley, 2025) Louafi, Meriem; Messaoudi, Mohammed; Abdeljawad, Thabet; Jarad, FahdThis paper explores an optimal control problem of weakly coupled abstract hyperbolic systems with missing initial data. Hyperbolic systems, known for their wave-like phenomena and complexity, become even more challenging with weak coupling between subsystems. The study introduces no-regret and low-regret control strategies to handle missing information and achieve optimal performance. By deriving the Euler-Lagrange optimality system, it characterizes these control approaches in the context of weak coupling. Additionally, the paper establishes the existence and uniqueness of a no-regret and low-regret control, emphasizing the influence of uncertain coupling parameters. These findings are optimal control strategies for abstract weakly coupled hyperbolic systems under uncertainty. Finally, as highlighted in our conclusion, future research could explore integrating memory effects through fractional derivatives to improve the modeling of viscoelasticity, diffusion with memory, and wave damping.Article Citation - WoS: 9Citation - Scopus: 12Unsteady Mhd Williamson Fluid Flow With the Effect of Bioconvection Over Permeable Stretching Sheet(Hindawi Ltd, 2022) Asjad, Muhammad Imran; Zahid, Muhammad; Ali, Bagh; Jarad, FahdThe unsteady flow of Williamson fluid with the effect of bioconvection in the heat and mass transfer occurring over a stretching sheet is investigated. A uniform magnetic field, thermal radiation, thermal dissipation, and chemical reactions are taken into account as additional effects. The physical problem is formulated in the form of a system of partial differential equations and solved numerically. For this purpose, similarity functions are involved to transmute these equations into corresponding ordinary differential equations. After that, the Runge-Kutta method with shooting technique is employed to evaluate the desired findings with the utilization of a MATLAB script. As a result, the effects of various physical parameters on the velocity, temperature, and nanoparticle concentration profiles as well as on the skin friction coefficient and rate of heat transfer are discussed with the aid of graphs and tables. The parameters of Brownian motion and thermophoresis are responsible for the rise in temperature and bioconvection Rayleigh number diminishes the velocity field. This study on nanofluid bioconvection has been directly applied in the pharmaceutical industry, microfluidic technology, microbial improved oil recovery, modelling oil and gas-bearing sedimentary basins, and many other fields. Further, to check the accuracy and validation of the present results, satisfactory concurrence is observed with the existing literature.Article Citation - WoS: 8Citation - Scopus: 10Aggregation Operators for Interval-Valued Intuitionistic Fuzzy Hypersoft Set With Their Application in Material Selection(Hindawi Ltd, 2022) Zulqarnain, Rana Muhammad; Siddique, Imran; Jarad, Fahd; Karamti, Hanen; Iampan, AiyaredThe intuitionistic fuzzy hypersoft set (IFHSS) is the most generalized form of the intuitionistic fuzzy soft set used to resolve uncertain and vague data in the decision-making process, considering the parameters' multi-sub-attributes. Aggregation operators execute a dynamic role in assessing the two prospect sequences and eliminating anxieties from this perception. This paper prolongs the IFHSS to interval-valued IFHSS (IVIFHSS), which proficiently contracts with hesitant and unclear data. It is the most potent technique for incorporating insecure data into decision-making (DM). The main objective of this research is to develop the algebraic operational laws for IVIFHSS. Furthermore, using the algebraic operational law, some aggregation operators (AOs) for IVIFHSS have been presented, such as interval-valued intuitionistic fuzzy hypersoft weighted average (IVIFHSWA) and interval-valued intuitionistic fuzzy hypersoft weighted geometric (IVIFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) technique is vigorous for material selection. However, conventional methods of MCGDM regularly provide inconsistent results. Based on the expected AOs, industrial enterprises propose a robust MCGDM material selection method to meet this shortfall. The real-world application of the planned MCGDM method for cryogenic storing vessel material selection (MS) is presented. The implication is that the designed model is more efficient and consistent in handling information based on IVIFHSS.Article Citation - WoS: 13Citation - Scopus: 11An Expanded Analysis of Local Fractionalintegral Inequalities Via Generalized (s,p)-Convexity(Springer, 2024) Li, Hong; Lakhdari, Abdelghani; Jarad, Fahd; Xu, Hongyan; Meftah, BadreddineThis research aims to scrutinize specific parametrized integral inequalities linked to 1,2, 3, and 4-point Newton-Cotes rules applicable to local fractional differentiable generalized (s,P)-convex functions. To accomplish this objective, we introduce a novel integral identity and deduce multiple integral inequalities tailored to mappings within the aforementioned function class. Furthermore, we present an illustrative example featuring graphical representations and potential practical applications.Article Citation - WoS: 7Citation - Scopus: 9An Exact and Comparative Analysis of Mhd Free Convection Flow of Water-Based Nanoparticles Via Cf Derivative(Hindawi Ltd, 2022) Aziz-Ur-Rehman, Aziz-Ur-; Riaz, Muhammad Bilal; Saeed, Syed Tauseef; Jarad, Fahd; Jasim, Hayder Natiq; Enver, Aytekin; Rehman, Aziz-Ur-Convective flow is a self-sustained flow with the effect of the temperature gradient. The density is nonuniform due to the variation in temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process, for instance, condensation, evaporation, and chemical process. Combination of water as base fluid and three types of nanoparticles named as copper, titanium dioxide, and aluminum oxide is taken into account. Due to the applications of the heat and mass transfer combined effects in different fields, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of MHD natural convection flow of water-based nano-particles in the presence of ramped conditions with Caputo-Fabrizio fractional time derivative. The exact fractional solutions of temperature, concentration, and velocity have been investigated by means of integral transform. The classical calculus is assumed as the instant rate of change of the output when the input level changes. Therefore, it is not able to include the previous state of the system called the memory effect. But, in the fractional calculus (FC), the rate of change is affected by all points of the considered interval to incorporate the previous history/memory effects of any system. Due to this reason, we applied the modern definition of fractional derivative. Here, the order of the fractional derivatives will be treated as an index of memory. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). Our results suggest that the incremental value of the M is observed for a decrease in the velocity field, which reflects to control resistive force.Article Quasilinear Coupled System in the Frame of Nonsingular Abc-Derivatives With P-Laplacian Operator at Resonance(Springer Basel Ag, 2024) Jarad, Fahd; Adjabi, Yassine; Panda, Sumati Kumari; Bouloudene, MokhtarWe investigate the existence of solutions for coupled systems of fractional p-Laplacian quasilinear boundary value problems at resonance given by the Atangana-Baleanu-Caputo (shortly, ABC) derivatives formulations are based on the well-known Mittag-Leffler kernel utilizing Ge's application of Mawhin's continuation theorem. Examples are provided to demonstrate our findings.Article Citation - WoS: 32Citation - Scopus: 33On the Multiparameterized Fractional Multiplicative Integral Inequalities(Springer, 2024) Saleh, Wedad; Lakhdari, Abdelghani; Jarad, Fahd; Meftah, Badreddine; Almatrafi, Mohammed BakheetWe introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for multiplicatively s-convex mappings in connection with different quadrature rules involving one, two, and three points. Our results cover both new findings and established ones, offering a holistic framework for comprehending these inequalities. To validate our outcomes, we provide an illustrative example with visual aids. Furthermore, we highlight the practical significance of our discoveries by applying them to special means of real numbers within the realm of multiplicative calculus.