Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Conference Object Citation - WoS: 2Citation - Scopus: 2Difference Discrete Variational Principles(Amer inst Physics, 2006) Baleanu, Dumitru; Jarad, FahdThe paper provides the discrete Lagrangian and Hamiltonian formulations of mechanical systems for both non-singular and singular cases. The Lagrangians with linear velocities and with higher velocities are investigated and the corresponding difference Euler-Lagrange equations and Hamiltonians are found.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.Article Citation - WoS: 14Citation - Scopus: 12Representation of Solutions for Sturm-Liouville Eigenvalue Problems With Generalized Fractional Derivative(Amer inst Physics, 2020) Bas, Erdal; Baleanu, Dumitru; Ozarslan, RamazanWe analyze fractional Sturm-Liouville problems with a new generalized fractional derivative in five different forms. We investigate the representation of solutions by means of rho-Laplace transform for generalized fractional Sturm-Liouville initial value problems. Finally, we examine eigenfunctions and eigenvalues for generalized fractional Sturm-Liouville boundary value problems. All results obtained are compared with simulations in detail under different alpha fractional orders and real rho values. Published under license by AIP Publishing.Article Citation - WoS: 47Citation - Scopus: 43Mathematical Modeling for Adsorption Process of Dye Removal Nonlinear Equation Using Power Law and Exponentially Decaying Kernels(Amer inst Physics, 2020) Yusuf, Abdullahi; Shaikh, Asif Ali; Inc, Mustafa; Baleanu, Dumitru; Qureshi, Sania; Ali Shaikh, AsifIn this research work, a new time-invariant nonlinear mathematical model in fractional (non-integer) order settings has been proposed under three most frequently employed strategies of the classical Caputo, the Caputo-Fabrizio, and the Atangana-Baleanu-Caputo with the fractional parameter chi , where 0 < chi <= 1. The model consists of a nonlinear autonomous transport equation used to study the adsorption process in order to get rid of the synthetic dyeing substances from the wastewater effluents. Such substances are used at large scale by various industries to color their products with the textile and chemical industries being at the top. The non-integer-order model suggested in the present study depicts the past behavior of the concentration of the solution on the basis of having information of the initial concentration present in the dye. Being nonlinear, it carries the possibility to have no exact solution. However, the Lipchitz condition shows the existence and uniqueness of the underlying model's solution in non-integer-order settings. From a numerical simulation viewpoint, three numerical techniques having first order convergence have been employed to illustrate the numerical results obtained. Published under license by AIP Publishing.Article Citation - WoS: 20Citation - Scopus: 21Stability Analysis and Numerical Simulations of Spatiotemporal Hiv Cd4+t Cell Model With Drug Therapy(Amer inst Physics, 2020) Elsonbaty, Amr; Adel, Waleed; Baleanu, Dumitru; Rafiq, Muhammad; Ahmed, NaumanIn this study, an extended spatiotemporal model of a human immunodeficiency virus (HIV) CD4+ T cell with a drug therapy effect is proposed for the numerical investigation. The stability analysis of equilibrium points is carried out for temporal and spatiotemporal cases where stability regions in the space of parameters for each case are acquired. Three numerical techniques are used for the numerical simulations of the proposed HIV reaction-diffusion system. These techniques are the backward Euler, Crank-Nicolson, and a proposed structure preserving an implicit technique. The proposed numerical method sustains all the important characteristics of the proposed HIV model such as positivity of the solution and stability of equilibria, whereas the other two methods have failed to do so. We also prove that the proposed technique is positive, consistent, and Von Neumann stable. The effect of different values for the parameters is investigated through numerical simulations by using the proposed method. The stability of the proposed model of the HIV CD4+ T cell with the drug therapy effect is also analyzed.Editorial Citation - WoS: 4Citation - Scopus: 4Preface: Recent Advances in Fractional Dynamics(Amer inst Physics, 2016) Baleanu, Dumitru; Li, Changpin; Srivastava, H. M.This Special Focus Issue contains several recent developments and advances on the subject of Fractional Dynamics and its widespread applications in various areas of the mathematical, physical, and engineering sciences. Published by AIP Publishing.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.Conference Object Reproducing Kernel Method for Strongly Non-Linear Equation(Amer inst Physics, 2018) Akgul, Esra Karatas; Baleanu, Dumitru; Akgul, AliIn this paper, we search the efficiency of the reproducing kernel method (RKM) in solving the strongly nonlinear equation. An example is presented to prove the power of the technique. The results attained from the technique are compared with the other techniques. Results prove that the presented technique is very effective.Conference Object Citation - WoS: 1Citation - Scopus: 2A Homotopy Perturbation Solution for Solving Highly Nonlinear Fluid Flow Problem Arising in Mechanical Engineering(Amer inst Physics, 2018) Akgul, Ali; Faraz, Naeem; Inc, Mustafa; Akgul, Esra Karatas; Baleanu, Dumitru; Khan, YasirIn this paper, a highly nonlinear equations are treated analytically via homotopy perturbation method for fluid mechanics problem. The non-linear differential equations are transformed to a coupled non-linear ordinary, differential equations via similarity transformations. Graphical results are presented and discussed for various physical parameters.