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: 180Citation - Scopus: 192On Fractional Calculus with General Analytic Kernels(Elsevier Science Inc, 2019) Fernandez, Arran; Ozarslan, Mehmet Ali; Baleanu, DumitruMany possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions. We demonstrate, under some assumptions, how all of these modifications can be considered as special cases of a single, unifying, model of fractional calculus. We provide a fundamental connection with classical fractional calculus by writing these general fractional operators in terms of the original Riemann-Liouville fractional integral operator. We also consider inversion properties of the new operators, prove analogues of the Leibniz and chain rules in this model of fractional calculus, and solve some fractional differential equations using the new operators. (C) 2019 Elsevier Inc. All rights reserved.Article Citation - WoS: 2Citation - Scopus: 5Analytic Studies of a Class of Langevin Differential Equations Dominated by a Class of Julia Fractal Functions(Univ Kragujevac, Fac Science, 2024) Ibrahim, Rabha W.; Baleanu, Dumitru. In this investigation, we study a class of analytic functions of type Carath & eacute;o dory style in the open unit disk connected with some fractal domains. This class of analytic functions is formulated based on a kind of Langevin differential equations (LDEs). We aim to study the analytic solvability of LDEs in the advantage of geometric function theory consuming the geometric properties of the Julia fractal (JF) and other fractal connected with the logarithmic function. The analytic solutions of the LDEs are obtainable by employing the subordination theory.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: 22Citation - Scopus: 25New Approach on Controllability of Hilfer Fractional Derivatives With Nondense Domain(Amer inst Mathematical Sciences-aims, 2022) Jothimani, Kasthurisamy; Ravichandran, Chokkalingam; Baleanu, Dumitru; Kumar, Devendra; Nisar, Kottakkaran SooppyThis work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Winch theorem and Banach contraction technique. In addition, a numerical approximation is given to deal with different criteria of our results.Article Citation - WoS: 7Citation - Scopus: 8Global Stability of Local Fractional Henon-Lozi Map Using Fixed Point Theory(Amer inst Mathematical Sciences-aims, 2022) Baleanu, Dumitru; Ibrahim, Rabha W.We present an innovative piecewise smooth mapping of the plane as a parametric discrete-time chaotic system that has robust chaos over a share of its significant organization parameters and includes the generalized Henon and Lozi schemes as two excesses and other arrangements as an evolution in between. To obtain the fractal Henon and Lozi system, the generalized Henon and Lozi system is defined by adopting the fractal idea (FHLS). The recommended system's dynamical performances are investigated from many angles, such as global stability in terms of the set of fixed points.Article Citation - WoS: 25Citation - Scopus: 27Finite Time Stability of Fractional Order Systems of Neutral Type(Mdpi, 2022) Baleanu, Dumitru; Ben Makhlouf, AbdellatifThis work deals with a new finite time stability (FTS) of neutral fractional order systems with time delay (NFOTSs). In light of this, FTSs of NFOTSs are demonstrated in the literature using the Gronwall inequality. The innovative aspect of our proposed study is the application of fixed point theory to show the FTS of NFOTSs. Finally, using two examples, the theoretical contributions are confirmed and substantiated.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: 9Citation - Scopus: 11Correcting Dimensional Mismatch in Fractional Models With Power, Exponential and Proportional Kernel: Application To Electrical Systems(Elsevier, 2022) Correa-Escudero, I. L.; Gomez-Aguilar, J. F.; Lopez-Lopez, M. G.; Alvarado-Martinez, V. M.; Baleanu, D.Fractional calculus is a powerful tool for describing diffusion phenomena, anomalous behaviors, and in general, systems with highly complex dynamics. However, the application of fractional operators for modeling purposes, produces a dimensional problem. In this paper, the fractional models of the RC, RL, RLC electrical circuits, a supercapacitor, a bank of supercapacitors, a LiFePO4 battery and a direct current motor are presented. A correction parameter is included in their formulation in order to preserve dimensionality in the physical equations. The optimal value of this parameter was determined via particle swarm optimization algorithm using numerical simulations and experimental data. Thus, a direct and effective approach for the construction of dimensionally corrected fractional models with power, exponential-decay and constant proportional Caputo hybrid derivative is presented. To show the effectiveness of the procedure, the time-response of the models is compared with experimental data and the modeling error is computed. The numerical solutions of the models were obtained using a numerical method based on the Adams methods.Article Citation - WoS: 6Citation - Scopus: 8The Dynamic and Discrete Systems of Variable Fractional Order in the Sense of the Lozi Structure Map(Amer inst Mathematical Sciences-aims, 2022) Natiq, Hayder; Baleanu, Dumitru; Ibrahim, Rabha W.; Al-Saidi, Nadia M. G.The variable fractional Lozi map (VFLM) and the variable fractional flow map are two separate systems that we propose in this inquiry. We study several key dynamics of these maps. We also investigate the sufficient and necessary requirements for the stability and asymptotic stability of the variable fractional dynamic systems. As a result, we provide VFLM with the necessary criteria to produce stable and asymptotically stable zero solutions. Furthermore, we propose a combination of these maps in control rules intended to stabilize the system. In this analysis, we take the 1D-and 2D-controller laws as givens.