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: 59Citation - Scopus: 66New Aspects of the Motion of a Particle in a Circular Cavity(Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; MatematikIn this work, we consider the free motion of a particle in a circular cavity. For this model, we obtain the classical and fractional Lagrangian as well as the fractional Hamilton's equations (FHEs) of motion. The fractional equations are formulated in the sense of Caputo and a new fractional derivative with Mittag-Leffler nonsingular kernel. Numerical simulations of the FHEs within these two fractional operators are presented and discussed for some fractional derivative orders. Numerical results are based on a discretization scheme using the Euler convolution quadrature rule for the discretization of the convolution integral. Simulation results show that the fractional calculus provides more flexible models demonstrating new aspects of the real-world phenomena.Article Citation - WoS: 81Citation - Scopus: 94The Fractional Dynamics of a Linear Triatomic Molecule(Editura Acad Romane, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Defterli, Özlem; Jajarmi, Amin; Defterli, Ozlem; Asad, Jihad H.; MatematikIn this research, we study the dynamical behaviors of a linear triatomic molecule. First, a classical Lagrangian approach is followed which produces the classical equations of motion. Next, the generalized form of the fractional Hamilton equations (FHEs) is formulated in the Caputo sense. A numerical scheme is introduced based on the Euler convolution quadrature rule in order to solve the derived FHEs accurately. For different fractional orders, the numerical simulations are analyzed and investigated. Simulation results indicate that the new aspects of real-world phenomena are better demonstrated by considering flexible models provided within the use of fractional calculus approaches.Article Citation - WoS: 43Citation - Scopus: 40Motion of a Particle in a Resisting Medium Using Fractional Calculus Approach(Editura Acad Romane, 2013) Rosales Garcia, J. Juan; Baleanu, Dumitru; Guia Calderon, M.; Martinez Ortiz, Juan; Baleanu, Dumitru; Garcia, J. Juan Rosales; Calderon, M. Guia; Ortiz, Juan Martinez; MatematikIn this manuscript we propose a fractional differential equation to describe the vertical motion of a body through the air. The order of the derivative was considered to be 0 < gamma <= 1. To keep the dimensionality of the physical parameter in the system, an auxiliary parameter sigma is introduced. This parameter characterizes the existence of fractional components in the given system. We prove that there is a relation between gamma and sigma through the physical parameter of the system and that, due to this relation the analytical solutions are given in terms of the Mittag-Leffler function depending on the order of the fractional differential equation.Article Citation - WoS: 20Citation - Scopus: 22Analytical Treatment of System of Abel Integral Equations by Homotopy Analysis Method(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; MatematikAbel equation has important applications in describing the least time for an object which is sliding on surface without friction in uniform gravity, and the classical theory of elasticity of materials is modeled by a system of Abel integral equations. In this manuscript, the homotopy analysis method is presented for obtaining analytical solutions of a system of Abel integral equations as fractional equations. The applied method has lessened the size of calculation and improved the accuracy of solution in the case of the singular Abel integral equation. The illustrated examples and numerical results have proved the assertion.Article Citation - WoS: 19Citation - Scopus: 20Fractional Calculus Analysis of the Cosmic Microwave Background(Editura Acad Romane, 2013) Tenreiro Machado, J. A.; Baleanu, Dumitru; Stefanescu, Petruta; Tintareanu, Ovidiu; Baleanu, Dumitru; MatematikCosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.Article Citation - WoS: 5Citation - Scopus: 7About Fractional Calculus of Singular Lagrangians(Fuji Technology Press Ltd, 2005) Baleanu, DumitruIn this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. We observed that if a Lagrangian is singular in the classical sense, it remains singular after being fractionally generalized. The fractional Lagrangian is non-local but its gauge symmetry was preserved despite complexity of equations in fractional cases. We generalized four examples of singular Lagrangians admitting gauge symmetry in fractional case and found solutions to corresponding Euler-Lagrange equations.Article Citation - Scopus: 1Finite Bivariate Biorthogonal N - Konhauser Polynomials(Taylor & Francis Ltd, 2025) Lekesiz, E. Guldogan; Cekim, B.; Ozarslan, M. A.; Güldoğan Lekesiz, E.A new set of finite 2D biorthogonal polynomials is defined using the finite orthogonal polynomials $ N_{n}<^>{\left (p\right ) }\left (w\right ) $ Nn(p)(w) and Konhauser polynomials. We present a connection between this finite 2D biorthogonal set and the generalized Laguerre-Konhauser polynomials. Also, we obtain several applications of finite bivariate biorthogonal N - Konhauser polynomials.Article Citation - WoS: 1Citation - Scopus: 1Fractional Systems With Multi-Parameters Fractional Derivatives(Springer, 2025) Muslih, S.I.; Agrawal, O.P.; Baleanu, D.Recently, a generalization of fractional variational formulations in terms of multiparameter fractional derivatives was introduced by Agrawal and Muslih. This treatment can be used to obtain the Lagrangian and Hamiltonian equations of motion. In this paper, we also extend our work to introduce the generalization of the formulation for constrained mechanical systems containing multi-parameter fractional derivatives. Three examples for regular and constrained fractional systems are analyzed. © The Author(s) 2025.