Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article On Multiplicative Fractional Operators of Hadamard and Katugampola Types in G-Calculus and Related Hermite-Hadamard Inequalities(World Scientific Publ Co Pte Ltd, 2026) Abdeljawad, Thabet; Lakhdari, Abdelghani; Jarad, Fahd; Budak, Hüseyin; Alqudah, Manar AThis paper explores the extension of classical fractional operators to the framework of G-calculus, a non-Newtonian calculus in which differentiation and integration are defined via multiplicative analogs of their classical counterparts. We begin by recalling key concepts from both fractional calculus and G-calculus. Next, we revisit the recently introduced multiplicative Riemann-Liouville fractional operators and extend the multiplicative Riemann-Liouville fractional derivative to arbitrary order alpha > 0. Building on this foundation, we introduce multiplicative versions of the Hadamard and Katugampola fractional integrals and derivatives. Finally, we establish Hermite-Hadamard inequalities for both newly defined integrals.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 Explicit Commutativity and Stability Theories for Second-Order Heun's LTVSs(World Scientific Publ Co Pte Ltd, 2025) Ibrahim, Salisu; Baleanu, DumitruThis paper derived and proved the simplex explicit commutativity theories and conditions for second-order linear time-varying systems (LTVSs) with both zero and nonzero initial conditions (ICs). We consider Heun's LTVS as a case study to verify the explicit commutative results, which were supported by simulation. Furthermore, we investigate the sensitivity of Heun's LTVS, the robustness of Heun's LTVS, the stability of Heun's LTVS, the effects due to disturbance on Heun's LTVS and the problem associated with commutativity of Heun's LTVS. These findings will tackle many problems related to the commutativity theory, the stability of LTVS, design and behavior of control systems, which have made an essential contribution and play a vital role in science and engineering. By considering a sinusoid of amplitude 5, bias -3 and frequency 7, with parameters c2,c1,c0 and an arbitrary choosing initial time (IT) t0 to be and also the initial states yA(0),yB(0),yA '(0),yB '(0), several quantitative results obtained by simulation show that the Heun's LTVSs AB and BA give the same output response, AB and BA are commutative under certain conditions and proved to be unstable numerically. Moreover, the quantitative results proved that the Heun's LTVSs AB and BA are very sensitive toward changes in ICs and parameters. Disturbance between the connections also affects the systems AB and BA, these give different responses as a result of tampering with the conditions, hence commutativity is not satisfied. Several examples have been given to support our fact explicitly and numerically. However, the explicit commutativity and stability for Heun's LTVS have not been in the literature yet, and this paper presents it for the first time. The results are well verified by simulation and treated with Wolfram Mathematica 11.Article 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: 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: 2Citation - Scopus: 2Job Flow Patterns and Productivity Dynamics in Turkish Manufacturing(World Scientific Publ Co Pte Ltd, 2024) Dogan, Ergun; Islam, M. Qamarul; Yazici, MehmetIn this paper, we analyze the job creation and destruction process, and the productivity dynamics in Turkish manufacturing by size, export status, import status and ownership by using a comprehensive firm-level dataset for the period of 2010-2015. Our focus is on the effect of turnover, which is due to the entry and exit of firms, on both job flows and industrial productivity growth. Our results show that while small firms contribute most to job creation, it is the large firms that contribute most to productivity growth. Regarding ownership, domestic private firms perform better than foreign firms in both job creation and productivity growth. With respect to export status, even though non-exporters outperform exporters in job creation, exporters dominate the productivity growth. As for import status, in job creation, like in the case of export status, non-importers do better but in productivity growth, unlike in the export status, no group of firms dominate, more specifically importers' and non-importers' contributions are close to each other. Another interesting finding is that, turnover effect on industry productivity is positive but very low. The role of incumbent firms in generating productivity growth is much higher than that of entering and exiting firms.Article Citation - WoS: 1A New Formulation and Analytical Applications of Fractional Operators(World Scientific Publ Co Pte Ltd, 2024) Mehmood, Ahsan; Samraiz, Muhammad; Liu, Zhi-Guo; Baleanu, Dumitru; Vivas-Cortez, MiguelThis research paper introduces a novel formulation of the modified Atangana-Baleanu (AB) Fractional Operators (FrOs). The paper begins by discussing the boundedness of the novel fractional derivative operator. Some fractional differential equations corresponding to different choices of functions as well as comparative graphical representations of a function and its derivative are provided. Furthermore, the paper investigates the generalized Laplace transform for this newly introduced operator. By employing the generalized Laplace transform, a wide range of fractional differential equations can be effectively solved. Additionally, the paper establishes the corresponding form of the AB Caputo fractional integral operator, examines its boundedness and obtains its Laplace transform. It is worth noting that the FrOs previously documented in the existing literature can be derived as special cases of these recently explored FrOs.Article Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems(World Scientific Publ Co Pte Ltd, 2025) Ibrahim, Salisu; Isah, Abdulnasir; Iqbal, Mujahid; Chang, Phang; Baleanu, DumitruIn this work, we present a comprehensive study of the commutativity of fractional-order linear time-varying systems (LTVSs). Commutativity is a fundamental property in the analysis and control of dynamic systems and is often used to simplify the design of controllers. Fractional-order systems, which are characterized by a noninteger-order derivative, have been widely studied in recent years due to their ability to model a wide range of phenomena. However, the commutativity of fractional-order LTVSs has not been widely explored. In this work, we present a comprehensive study of the commutativity of fractional-order LTVSs. We first provide a mathematical definition of commutativity for these systems and demonstrate that it is equivalent to the commutativity of their transfer functions. We then propose a method for verifying the general condition for commutativity of fractional-order LTVSs under zero initial conditions (ICs) and prove it mathematically. Based on our findings, we realized that the commutative requirements, properties, theories, and conditions are general for fractional-order LTVSs, please observed that some fractional-order LTVSs are commutative, some are not commutative, while some are commutative under certain conditions. Based on this fact, we can say that not all fractional-order LTVSs are commutative.We apply explicit commutative results to several examples of fractional-order LTVSs. Our theoretical and simulation results show a good agreement and prove that our fractional-order LTVSs are commutative under certain conditions, moreover, the commutativity property holds for certain conditions and classes of fractional-order LTVSs, but not for others. Because of the application of fraction commutativity in various fields of science and engineering, we find it necessary to come up with explicit results for the first time.Editorial Citation - WoS: 1Citation - Scopus: 1Editorial Special Issue Section on Fractal Ai-Based Analyses and Applications To Complex Systems: Part Ii(World Scientific Publ Co Pte Ltd, 2022) Karaca, Yeliz; Baleanu, Dumitru; Moonis, Majaz; Muhammad, Khan; Zhang, Yu-Dong; Gervasi, Osvaldo