WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 8Citation - Scopus: 9The Numerical Solution of Fourth Order Nonlinear Singularly Perturbed Boundary Value Problems Via 10-Point Subdivision Scheme Based Numerical Algorithm(Amer inst Physics, 2020) Baleanu, Dumitru; Mustafa, Ghulam; Malik, Safia; Chu, Yu-Ming; Ejaz, Syeda TehminaThe subdivision scheme is used to illustrate smooth curves and surfaces. It is an algorithmic technique which takes a coarse polygon as an input and produces a refined polygon as an output. In this paper, a 10-point interpolating subdivision scheme is used to develop a numerical algorithm for the solution of fourth order nonlinear singularly perturbed boundary value problems (NSPBVPs). The studies of convergence and approximation order of the numerical algorithm are also presented. The solution of NSPBVPs is presented to see the efficiency of the algorithm.Article Citation - WoS: 29Citation - Scopus: 28The General Bilinear Techniques for Studying the Propagation of Mixed-Type Periodic and Lump-Type Solutions in a Homogenous-Dispersive Medium(Amer inst Physics, 2020) Osman, Mohamed S.; Zhu, Wen-Hui; Zhou, Li; Baleanu, Dumitru; Liu, Jian-GuoThis paper aims to construct new mixed-type periodic and lump-type solutions via dependent variable transformation and Hirota's bilinear form (general bilinear techniques). This study considers the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves in a homogeneous medium in fluid dynamics. The obtained solutions contain abundant physical structures. Consequently, the dynamical behaviors of these solutions are graphically discussed for different choices of the free parameters through 3D plots.Editorial Citation - WoS: 2Citation - Scopus: 2Comment on "maxwell's Equations and Electromagnetic Lagrangian Density in Fractional Form" [J. Math. Phys. 53, 033505 ( 2012)](Amer inst Physics, 2014) Al-Jamel, A.; Widyan, H.; Baleanu, D.; Rabei, Eqab M.In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)]. (C) 2014 AIP Publishing LLC.Article Citation - WoS: 36Citation - Scopus: 35Traveling Wave Solutions and Conservation Laws for Nonlinear Evolution Equation(Amer inst Physics, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, DumitruIn this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated. Published by AIP Publishing.Article Citation - WoS: 79Citation - Scopus: 94Existence and Uniqueness Theorem for a Class of Delay Differential Equations With Left and Right Caputo Fractional Derivatives(Amer inst Physics, 2008) Abdeljawad, Thabet; Baleanu, Dumitru; Jarad, Fahd; Maraaba, ThabetThe existence and uniqueness theorems for functional right-left delay. and left-right advanced fractional functional differential equations with bounded delay and advance, respectively, are proved. The continuity with respect to the initial function for these equations is also proved under some Lipschitz kind conditions. The Q-operator is used to transform the delay-type equation to an advanced one and vice versa. An example is given to clarify the results. (C) 2008 American Institute Of Physics.Article Citation - WoS: 13Citation - Scopus: 12Magnetohydrodynamic Mixed Convection Flow of Jeffery Fluid With Thermophoresis, Soret and Dufour Effects and Convective Condition(Amer inst Physics, 2019) Baleanu, Dumitru; Husnine, S. M.; Shabbir, Khurram; Iftikhar, NazishThe aim of this paper is to investigate heat and mass transfer of Jeffery fluid on a stretching sheet. Moreover, the influence of magnetic field with mixed convection, convective boundary condition and Soret and Dufour effects is also brought into the consideration along with chemical reaction and thermophoresis condition. The problem is modeled by system of partial differential equations and solutions are obtained by optimal homotopy analysis method. In addition, for comprehensive interpretation of the influence of the system parameters results are shown by graphs and tables. (C) 2019 Author(s).Article Citation - WoS: 15Citation - Scopus: 18Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics(Amer inst Physics, 2011) Vacaru, Sergiu I.; Baleanu, DumitruMethods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric data for such models are encoded into (fractional) bi-Hamiltonian structures and associated solitonic hierarchies. The constructions yield horizontal/vertical pairs of fractional vector sine-Gordon equations and fractional vector mKdV equations when the hierarchies for corresponding curve fractional flows are described in explicit forms by fractional wave maps and analogs of Schrodinger maps. (C) 2011 American Institute of Physics. [doi:10.1063/1.3589964]Article Citation - WoS: 1Citation - Scopus: 1Dualization of the Principal Sigma Model(Amer inst Physics, 2008) Yilmaz, Nejat T.; Ylmaz, Nejat T.The first-order formulation of the principal sigma model with a Lie group target space is performed. By using the dualization of the algebra and the field content of the theory the field equations which are solely written in terms of the field strengths are realized through an extended symmetry algebra parametrization. The structure of this symmetry algebra is derived so that it generates the realization of the field equations in a Bianchi identity of the current derived from the extended parametrization. (c) 2008 American Institute of Physics.