Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - Scopus: 1Study of Impulsive Problem with Caputo Fractional Derivative Involving Nonlocal Conditions Using Fixed Point Theory(Kyungnam University Press, 2025) Dhandapani, Swathi; Umapathi, Karthik Raja; Mathuraiveeran, Jeyaraman; Shah, Kamal; Abdeljawad (Maraaba) T., Thabet; Jarad, Fahd; Abdeljawad, ThabetIn this article, we study the existence of solutions for an impulsive Caupto fractional differential equations with a class of initial value problem dependence on the Lipschitz first derivative conditions. Our main tool is a Banach's fixed point theorem and Leray-Schauder fixed point theorem. We also investigate the existence of fractional Derivative with non-local conditions. An numerical example is given to clarify the results. © 2025 Elsevier B.V., All rights reserved.Article Citation - WoS: 5Citation - Scopus: 5Performance Evaluation of Matched Asymptotic Expansions for Fractional Differential Equations With Multi-Order(Soc Matematice Romania, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Sayevand, Khosro; MatematikAn extension of the concept of the asymptotic expansions method is presented in this paper. The multi-order differential equations of fractional order are investigated and the convergence of the proposed method is proven. The reported results show that the present approach is very effective and accurate and also are in good agreement with the ones in the literature.Article Citation - WoS: 16Citation - Scopus: 23On Fractional Hamiltonian Systems Possessing First-Class Constraints Within Caputo Derivatives(Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; MatematikThe fractional constrained systems possessing only first class constraints are analyzed within Caputo fractional derivatives. It was proved that the fractional Hamilton-Jacobi like equations appear naturally in the process of finding the full canonical transformations. An illustrative example is analyzed.Article Citation - Scopus: 61Solving Multi-Term Orders Fractional Differential Equations by Operational Matrices of Bps With Convergence Analysis(2013) Rostamy, D.; Baleanu, Dumitru; Alipour, M.; Jafari, H.; Baleanu, D.; MatematikIn this paper, we present a numerical method for solving a class of fractional differential equations (FDEs). Based on Bernstein Polynomials (BPs) basis, new matrices are utilized to reduce the multi-term orders fractional differential equation to a system of algebraic equations. Convergence analysis is shown by several theorems. Illustrative examples are included to demonstrate the validity and applicability of this method.Article Citation - Scopus: 3On Some Impulsive Fractional Neutral Differential Systems With Nonlocal Condition Through Fractional Operators(Cambridge Scientific Publishers, 2017) Anuradha, A.; Baleanu, Dumitru; Baleanu, D.; Suganya, S.; Arjunan, M.M.; MatematikAccording to semigroup theories, fractional calculus, Banach contraction principle and Schaefer's fixed point theorem, this paper is fundamentally involved with the existence of mild solutions for an impulsive fractional neutral differential systems (abbreviated, IFNDS) with nonlocal conditions (abbreviated, NLC) in Banach space X. At last, an illustration is also presented to exhibit the use of our theoretical results. © CSP - Cambridge, UK; I & S - Florida, USA, 2017.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 - Scopus: 1Analysis of Fractional Fokker-Planck Equation With Caputo and Caputo-Fabrizio Derivatives(Univ Craiova, 2021) Cetinkaya, Suleyman; Baleanu, Dumitru; Demir, Ali; Baleanu, Dumitru; MatematikThis research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used together. By SHAM analytical series solution of any mathematical model including fractional derivative can be obtained. By this method, we constructed the solution of fractional Fokker-Planck equations in Caputo and Caputo-Fabrizio senses. The results show that this method is advantageous and applicable to form the series resolution of the fractional mathematical models.Article Citation - WoS: 29Citation - Scopus: 31A Novel Spectral Approximation for the Two-Dimensional Fractional Sub-Diffusion Problems(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Zaky, M. A.; Baleanu, D.; Abdelkawy, M. A.; MatematikThis paper reports a new numerical method that enables easy and convenient discretization of a two-dimensional sub-diffusion equation with fractional derivatives of any order. The suggested method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional derivatives, described in the Caputo sense. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. The validity and effectiveness of the method are demonstrated by solving two numerical examples, which are presented in the form of tables and graphs to make more easier comparisons with the exact solutions and the results obtained by other methods.Article Citation - WoS: 5Citation - Scopus: 6Application of Sumudu and Double Sumudu Transforms To Caputo-Fractional Differential Equations(Eudoxus Press, Llc, 2012) Jarad, Fahd; Jarad, Fahd; Tas, K.; Taş, Kenan; MatematikThe definition, properties and applications of the Sumudu transform to ordinary differential equations are described in [1-3]. In this manuscript we derive the formulae for the Sumudu and double Sumudu transforms of ordinary and partial fractional derivatives and apply them in solving Caputo-fractional differential equations. Our purpose here is to show the applicability of this new transform and its efficiency in solving such problems.