Scopus İndeksli Yayınlar Koleksiyonu
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Editorial Preface(de Gruyter, 2019) Baleanu, Dumitru; Lopes, António Mendes; Hristov, Jordan; Anastassiou, George A.; Karapınar, Erdal; Salim, Abdelkrim; Benchohra, Mouffak; Singh, Jagdev; Cattani, Carlo; Kumar, Devendra; Dutta, Hemen; Lazreg, Jamal EddineEditorial Preface(de Gruyter, 2019) Baleanu, Dumitru; Lopes, António MendesArticle Population Dynamic Caused by War Involvement via Fractional Derivative on Time Scales(Inderscience Publishers, 2019) Baleanu, Dumitru; Agheli, Bahram; Neamaty, Abdolali; Nategh, MehdiArticle Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay(MDPI AG, 2019) Baleanu, Dumitru; Shah, Rasool; Arif, Muhammad; Khan, Hassan; Kumam, PoomArticle 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: 14Citation - Scopus: 18Existence Theory and Numerical Simulation of HIV-I Cure Model with New Fractional Derivative Possessing a Non-Singular Kernel(Springeropen, 2019) Aliyu, Aliyu Lsa; Alshomrani, Ali Saleh; Li, Yongjin; Inc, Mustafa; Baleanu, DumitruIn this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana-Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard-Lindelof has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.Article Citation - WoS: 3Citation - Scopus: 3Existence Results for Block Matrix Operator of Fractional Orders in Banach Algebras(MDPI, 2019) Hashem, Hind; El-Sayed, Ahmed; Baleanu, DumitruThis paper is concerned with proving the existence of solutions for a coupled system of quadratic integral equations of fractional order in Banach algebras. This result is a direct application of a fixed point theorem of Banach algebras. Some particular cases, examples and remarks are illustrated. Finally, the stability of solutions for that coupled system are studied.Article Citation - WoS: 3Citation - Scopus: 2Surface Terms, Angular Momentum and Hamilton-Jacobi Formalism(Soc Italiana Fisica, 2003) Güler, Y; Baleanu, Dumitru; Baleanu, D; Cenk, M; MatematikQuadratic Lagrangians are introduced adding surface terms to a free-particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of a constrained system. The manifold structure induced by the quadratic Lagrangian is investigated.Article Citation - WoS: 36Citation - Scopus: 41Numerical Treatment of Coupled Nonlinear Hyperbolic Klein-Gordon Equations(Editura Acad Romane, 2014) Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; Baleanu, D.; Abdelkawy, M. A.; MatematikA semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GL-C) method is proposed and developed for the numerical solution of the spatial variable for two nonlinear coupled Klein-Gordon (KG) partial differential equations. The general Jacobi-Gauss-Lobatto points are used as collocation nodes in this approach. The main characteristic behind the J-GL-C approach is that it reduces such problems to solve a system of ordinary differential equations (SODEs) in time. This system is solved by diagonally-implicit Runge-Kutta-Nystrom scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.Article Citation - Scopus: 4On Mild Solution of Abstract Neutral Fractional Order Impulsive Differential Equations With Infinite Delay(Eudoxus Press, LLC, 2018) Anguraj, A.; Baleanu, Dumitru; Kanjanadevi, S.; Baleanu, D.; MatematikWe prove the existence and uniqueness of fractional neutral impulsive differential equations with infinite delay via contraction mapping principle and fixed point technique for condensing map. We use the resolvent operator technique for integral equations to make the mild solution of the problem more appropriate. © 2018 by Eudoxus Press, LLC. All rights reserved.