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 Citation - WoS: 105Citation - Scopus: 118On an Extension of the Operator With Mittag-Leffler Kernel(World Scientific Publ Co Pte Ltd, 2022) Baleanu, Dumitru; Al-Refai, MohammedDealing with nonsingular kernels is not an easy task due to their restrictions at origin. In this short paper, we suggest an extension of the fractional operator involving the Mittag-Leffler kernel which admits integrable singular kernel at the origin. New solutions of the related differential equations were reported together with some perspectives from the modelling viewpoint.Article Citation - WoS: 1Citation - Scopus: 1Heat Transfer of Mhd Oldroyd-B Fluid With Ramped Wall Velocity and Temperature in View of Local and Nonlocal Differential Operators(World Scientific Publ Co Pte Ltd, 2022) Riaz, Muhammad Bilal; Jarad, Fahd; Asgir, Maryam; Zafar, Azhar AliThe theoretical study focuses on the examination of the convective flow of Oldroyd-B fluid with ramped wall velocity and temperature. The fluid is confined on an extended, unbounded vertical plate saturated within the permeable medium. To depict the fluid flow, the coupled partial differential equations are settled by using the Caputo (C) and Caputo Fabrizio (CF) differential time derivatives. The mathematical analysis of the fractionalized models of fluid flow is performed by Laplace transform (LT). The complexity of temperature and velocity profile is explored by numerical inversion algorithms of Stehfest and Tzou. The fractionalized solutions of the temperature and velocity profile have been traced out under fractional and other different parameters considered. The physical impacts of associated parameters are elucidated with the assistance of the graph using the software MATHCAD 15. We noticed the significant influence of the fractional parameter (memory effects) and other parameters on the dynamics of the fluid flow. Shear stress at the wall and Nusselt number also are considered. It's brought into notice the fractional-order model (CF) is the best fit in describing the memory effects in comparison to the C model. An analysis of the comparison between the solution of velocity and temperature profile for ramped wall temperature and velocity and constant wall temperature and velocity is also performed.Article Citation - WoS: 8Citation - Scopus: 8A Novel Fractional Grey Model Applied To the Environmental Assessment in Turkey(World Scientific Publ Co Pte Ltd, 2020) Arshad, Sadia; Defterli, Ozlem; Xie, Xiaoqing; Baleanu, Dumitru; Shaheen, Aliya; Sheng, JinyongThis study presents a novel fractional order grey model FGM (alpha,1) obtained by extending the grey model (GM (1,1)). For this, we generalize the whitenization first-order differential equation to fractional order by using the Caputo fractional derivative of order alpha. A real-world case study, scrutinize the economic growth influence on environmental degradation in Turkey, is performed to evaluate the significance of the projected model FGM (alpha,1) in contrast to the current classical GM. We apply autoregressive distributed lags bounds testing co-integration approach to empirically examine the long-run and short-run relation among economic growth, agriculture, forestry and fishing (AFF), electricity utilization and CO2 emissions. Using the new fractional order model, all the variables are forecasted in the forthcoming years until 2030. Findings disclose that electricity utilization and economic growth (GDP) accelerate emission of CO2 though in the long run agriculture, forestry, and fishing reduce the environmental pollution in Turkey.Article Citation - WoS: 35Citation - Scopus: 44Generalized Fractional Order Bloch Equation With Extended Delay(World Scientific Publ Co Pte Ltd, 2012) Daftardar-Gejji, Varsha; Baleanu, Dumitru; Magin, Richard; Bhalekar, SachinThe fundamental description of relaxation (T-1 and T-2) in nuclear magnetic resonance (NMR) is provided by the Bloch equation, an integer-order ordinary differential equation that interrelates precession of magnetization with time-and space-dependent relaxation. In this paper, we propose a fractional order Bloch equation that includes an extended model of time delays. The fractional time derivative embeds in the Bloch equation a fading power law form of system memory while the time delay averages the present value of magnetization with an earlier one. The analysis shows different patterns in the stability behavior for T-1 and T-2 relaxation. The T-1 decay is stable for the range of delays tested (1 mu sec to 200 mu sec), while the T-2 relaxation in this extended model exhibits a critical delay (typically 100 mu sec to 200 mu sec) above which the system is unstable. Delays arise in NMR in both the system model and in the signal excitation and detection processes. Therefore, by adding extended time delay to the fractional derivative model for the Bloch equation, we believe that we can develop a more appropriate model for NMR resonance and relaxation.Article Citation - WoS: 9Citation - Scopus: 8Fractional Time Action and Perturbed Gravity(World Scientific Publ Co Pte Ltd, 2011) Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab; Sadallah, MadhatIn this paper, we used the scaling concepts of Mandelbrot of fractals in variational problems of mechanical systems in order to re-write the action integral function as an integration over the fractional time. In addition, by applying the variational principle to this new fractional action, we obtained the modified Euler-Lagrange equations of motion in any fractional time of order 0 < alpha <= 1. Two examples are investigated in detail.Article Citation - WoS: 2Citation - Scopus: 5Fractional Euler-Lagrange and Fractional Hamilton Equations for Super Symmetric Classical Model(World Scientific Publ Co Pte Ltd, 2007) Muslih, Sami I.; Baleanu, DumitruFractional Euler-Lagrange equations were investigated in the presence of the elements of Berezin algebra. The super fractional Hessian was defined and the fractional Hamiltonian of the super symmetric classical model was constructed.