Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1Multiplicative Tempered Fractional Integrals in G-Calculus and Associated Hermite-Hadamard Inequalities(World Scientific Publ Co Pte Ltd, 2026) Lakhdari, Abdelghani; Saleh, Wedad; Budak, Huseyin; Meftah, Badreddine; Jarad, FahdThis paper introduces the first theory of tempered fractional integrals within the framework of G-calculus, a multiplicative non-Newtonian system for positive-valued functions with positive arguments. We begin by formulating the multiplicative Riemann-Liouville integral in its pure multiplicative form and extend it to include an exponential tempering parameter. A new multiplicative lambda-incomplete Gamma function is defined to characterize these operators. Furthermore, we introduce and analyze multiplicative convexity in G-calculus, along with novel multiplicative formulations of the classical midpoint and trapezoidal quadrature rules. We then establish the Hermite-Hadamard inequalities for GG-convex functions and derive two novel multiplicative integral identities, leading to midpoint- and trapezium-type bounds. Numerical examples with graphical illustrations, applications to quadrature rules, and connections to special means validate our results. The proposed framework fills a critical gap in non-Newtonian analysis and provides new tools for modeling scale-invariant phenomena in economics, biology, and signal processing.Article On the Finite Delayed Fractional Differential Equation via the Weighted Riemann-Liouville Derivative of Variable Order(World Scientific Publ Co Pte Ltd, 2026) Jarad, Fahd; Abdeljawad, Thabet; Souid, Mohammed Said; Hallouz, Abdelhamid; Alqudah, ManarThis study investigates the existence and uniqueness of solutions to initial value problems for nonlinear variable-order weighted fractional differential equations with finite delay. Building upon and generalizing prior constant-order fractional models, our approach employs fixed-point theory, specifically the Banach and Schauder fixed-point theorems, in suitable weighted function spaces to rigorously establish these fundamental results. We further demonstrate the applicability of our theoretical framework through illustrative examples. The findings contribute significantly to the mathematical understanding and modeling capabilities of complex systems exhibiting memory and hereditary properties governed by variable-order fractional dynamics.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: 6Citation - Scopus: 6Modeling the Transmission Dynamics of Middle Eastern Respiratory Syndrome Coronavirus with the Impact of Media Coverage(Elsevier, 2021) Fatima, BiBi; Alqudah, Manar A.; Zaman, Gul; Jarad, Fahd; Abdeljawad, ThabetMiddle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R-0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.Correction Corrigendum To “Numerical Investigation of Magneto-Thermal Impact on Phase Change Phenomenon of Nano-PCM Within a Hexagonal Shaped Thermal Energy Storage” [Appl. Thermal Eng., (2023) 223, 119984](s1359431123000133)(10.1016/J.applthermaleng.2023.119984)(Pergamon-Elsevier Science Ltd, 2025) Izadi, Mohsen; Sheremet, Mikhail; Hajjar, Ahmad; Galal, Ahmed M.; Mahariq, Ibrahim; Jarad, Fahd; Hamida, Mohamed Bechir Ben; Ben Hamida, Mohamed BechirArticle Weighted Fractional Proportional Operators Regarding a Function and Their Hilfer Unification(World Scientific Publ Co Pte Ltd, 2025) Othmane, Iman ben; Abdeljawad, Thabet; Jarad, FahdIn this paper, some new forms of fractional operators are proposed. These new forms are developed by using the proportional and the weighted derivative of a function regarding a function, known as weighted fractional proportional operators regarding another function. Additionally, the partial derivative-Hilfer version of the weighted proportional fractional derivatives, which is a concept that unifies the Riemann-Liouville and Caputo weighted proportional fractional derivatives, is propounded. Moreover, a number of fundamental properties of these operators and related important results are investigated. The Laplace transforms of the newly defined operators are found. Finally, we solve a particular type of differential equations involving the introduced derivatives in favor of the weighted Laplace transform.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: 4Citation - Scopus: 4On Conformable Fractional Newton-Type Inequalities(World Scientific Publ Co Pte Ltd, 2025) Xu, Hongyan; Awan, Muhammad uzair; Meftah, Badreddine; Jarad, Fahd; Lakhdari, AbdelghaniBy using a parametrized analysis, this paper presents a study that focuses on examining both the Simpson's 3/8 formula and the corrected Simpson's 3/8 formula. By utilizing a unique identity that incorporates conformable fractional integral operators, we have constructed novel conformable Newton-type inequalities for functions that possess second-order s-convex derivatives. Special cases are extensively discussed, and the accuracy of the results is validated through a numerical example with graphical representations.Article Citation - WoS: 23Citation - Scopus: 23Ostrowski Type Inequalities Via New Fractional Conformable Integrals(Amer inst Mathematical Sciences-aims, 2019) Set, Erhan; Akdemir, Ahmet Ocak; Gozpinar, Abdurrahman; Jarad, Fahd; Rashid, Saima; Safdar, Farhat; Noor, Muhammad Aslam; Noor, Khalida InayatIn this present study, firstly, some necessary definitions and some results related to Riemann-Liouville fractional and new fractional conformable integral operators defined by Jarad et al. [13] are given. As a second, a new identity has been proved. By using this identity, new Ostrowski type inequalities has obtained involving fractional conformable integral operators. Also, some new inequalities has established for AG-convex functions via fractional conformable integrals in this study. Relevant connections of the results presented here with those earlier ones are also pointed out.Article Citation - WoS: 18Citation - Scopus: 19The General Caputo-Katugampola Fractional Derivative and Numerical Approach for Solving the Fractional Differential Equations(Elsevier, 2025) Sadek, Lakhlifa; Ldris, Sahar Ahmed; Jarad, FahdIn this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the psi-Caputo-Katugampola fractional derivative (psi-CKFD). The Caputo-Katugampola (CKFD), the Caputo (CFD), and the Caputo-Hadamard FD (CHFD) are all special cases of this new fractional derivative. We also introduce the psi-Katugampola fractional integral (psi-KFI) and discuss several related theorems. An existence and uniqueness theorem for a psi-Caputo-Katugampola fractional Cauchy problem (psi-CKFCP) is established. Furthermore, we present an adaptive predictor-corrector algorithm for solving the psi-CKFCP. We include examples and applications to illustrate its effectiveness. The derivative used in our approach is significantly influenced by the parameters delta, gamma, and the function psi, which makes it a valuable tool for developing fractional calculus models.