Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Green’s Function and an Inequality of Lyapunov-Type for Conformable Boundary Value Problem(Institute of Mathematics, 2021) Basua, D.; Jonnalagadda, J.M.; Baleanu, D.In this article, we consider a conformable boundary value problem associated with Robin type boundary conditions and present a Lyapunov-type inequality for the same. Further, we attain a lower bound on the smallest eigenvalue for the corresponding conformable eigenvalue problem using the established result, semi maximum norm and Cauchy– Schwartz inequality. © 2021, Institute of Mathematics. All rights reserved.Article Citation - WoS: 66Citation - Scopus: 79Structure of Optical Soliton Solution for Nonliear Resonant Space-Time Schrodinger Equation in Conformable Sense With Full Nonlinearity Term(Iop Publishing Ltd, 2020) Al-Smadi, Mohammed; Al-Omari, Shrideh; Baleanu, Dumitru; Momani, Shaher; Alabedalhadi, MohammedNonclassical quantum mechanics along with dispersive interactions of free particles, long-range boson stars, hydrodynamics, harmonic oscillator, shallow-water waves, and quantum condensates can be modeled via the nonlinear fractional Schrodinger equation. In this paper, various types of optical soliton wave solutions are investigated for perturbed, conformable space-time fractional Schrodinger model competed with a weakly nonlocal term. The fractional derivatives are described by means of conformable space-time fractional sense. Two different types of nonlinearity are discussed based on Kerr and dual power laws for the proposed fractional complex system. The method employed for solving the nonlinear fractional resonant Schrodinger model is the hyperbolic function method utilizing some fractional complex transformations. Several types of exact analytical solutions are obtained, including bright, dark, singular dual-power-type soliton and singular Kerr-type soliton solutions. Moreover, some graphical simulations of those solutions are provided for understanding the physical phenomena.Article Solitons and Conservation Laws for the (2+1)-Dimensional Davey-Stewartson Equations with Conformable Derivative(2018) Yusuf, Abdullahi; İnç, Mustafa; Aliyu, Aliyu Isa; Baleanu, DumitruThis research obtains some new solitons for the Davey-Stewartson equation (DSE) with conformable derivative. The well known projective Ricatti equation ansatz (PREA) is employed to reach such solitons. The constraints conditions for the existence of soliton solutions are reported. Moreover, the conservation laws (Cls) for the governing equation is studied via multiplier technique. Physical features of some solutions are illustrated in Figures 1-8.Article Citation - WoS: 12Citation - Scopus: 16Soliton Solutions of Nonlinear Boussinesq Models Using the Exponential Function Technique(Iop Publishing Ltd, 2021) Baleanu, Dumitru; Nawaz, Sidra; Rezazadeh, Hadi; Javeed, ShumailaThis paper deals with the new analytical solutions of conformable nonlinear Boussinesq equations. Boussinesq equation is one of the important equation in the field of applied mathematics and engineering, particularly in optical fibers, plasma physics, fluid dynamics, signal processing, and shallow water etc. The focus of this paper is to obtain the new explicit solutions of conformable Boussinesq equations. Exponential function technique is employed to solve the considered models. The conformable properties are utilized to obtain new analytical solutions for this type of nonlinear Boussinesq equations. The new analytical solutions are acquired especially for the space-time boussinesq equation. The results are shown graphically. The obtained solutions can be useful for engineers and physicists to further analyze the phenomena. The implemented technique is valuable for finding new analytical solutions of nonlinear partial differential equations (PDEs).Article Citation - WoS: 34Citation - Scopus: 35On Well-Posedness of the Sub-Diffusion Equation With Conformable Derivative Model(Elsevier, 2020) Tran Bao Ngoc; Baleanu, Dumitru; O'Regan, Donal; Nguyen Huy Tuan; Ngoc, Tran Bao; Tuan, Nguyen HuyIn this paper, we study an initial value problem for the time diffusion equation (C)partial derivative(beta)/partial derivative t(beta) u + Au = F, 0 < beta <= 1, on Omega x (0, T), where the time derivative is the conformable derivative. We study the existence and regularity of mild solutions in the following three cases with source term F: F = F (x, t), i.e., linear source term; F = F (u) is nonlinear, globally Lipchitz and uniformly bounded. The results in this case play important roles in numerical analysis. F = F (u) is nonlinear, locally Lipchitz and uniformly bounded. The analysis in this case can be widely applied to many problems such as - Time Ginzburg-Landau equations C partial derivative(beta)u/partial derivative t(beta)+ (-Delta)u = vertical bar u vertical bar(mu-1) u; - Time Burgers equations C partial derivative(beta)u/partial derivative t(beta)-( u center dot del) u + (- Delta)u = 0; etc. (C) 2020 Elsevier B.V. All rights reserved.Article Citation - WoS: 7Citation - Scopus: 6On a Problem for the Nonlinear Diffusion Equation With Conformable Time Derivative(Taylor & Francis Ltd, 2022) Baleanu, Dumitru; Zhou, Yong; Huu Can, Nguyen; Au, Vo VanIn this paper, we study a nonlinear diffusion equation with conformable derivative: D-t((alpha)) u = Delta u = L(x, t; u(x, t)), where 0 < alpha < 1, (x, t) is an element of Omega x (0, T). We consider both of the problems: Initial value problem: the solution contains the integral I = integral(t)(0) tau(gamma) d tau (critical as gamma <= -1). Final value problem: not well-posed (if the solution exists it does not depend continuously on the given data). For the initial value problem, the lack of convergence of the integral I, for gamma <= -1. The existence for the solution is represented. For the final value problem, the Hadamard instability occurs, we propose two regularization methods to solve the nonlinear problem in case the source term is a Lipschitz function. The results of existence, uniqueness and stability of the regularized problem are obtained. We also develop some new techniques on functional analysis to propose regularity estimates of regularized solution.Article Citation - WoS: 10Citation - Scopus: 15Extension of Perturbation Theory To Quantum Systems With Conformable Derivative(World Scientific Publ Co Pte Ltd, 2021) Rabei, Eqab M.; Al-Jamel, Ahmed; Baleanu, Dumitru; Al-Masaeed, MohamedIn this paper, the perturbation theory is extended to be applicable for systems containing conformable derivative of fractional order alpha. This is needed as an essential and powerful approximation method for describing systems with conformable differential equations that are difficult to solve analytically. The work here is derived and discussed for the conformable Hamiltonian systems that appears in the conformable quantum mechanics. The required alpha-corrections for the energy eigenvalues and eigenfunctions are derived. To demonstrate this extension, three illustrative examples are given, and the standard values obtained by the traditional theory are recovered when alpha = 1.Article Citation - WoS: 40Citation - Scopus: 41Dark and Singular Optical Solitons for the Conformable Space-Time Nonlinear Schrodinger Equation With Kerr and Power Law Nonlinearity(Elsevier Gmbh, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, MustafaThis paper extracts novel dark and singular optical solitons for the conformable space time nonlinear Schrodinger equation (CSTNLSE) with Kerr and power law nonlinearity by two integration schemes. The integration schemes are generalized tanh (GT), and Bernoulli (BL) sub-ODE methods. The constraints conditions for the existence of solitons are reported. The newly introduced fractional derivative called conformable derivative is used for extracting the soliton solutions. Numerical simulations of some of the obtained solutions are also presented. (C) 2018 Elsevier GmbH. All rights reserved.Article Citation - WoS: 1Optical Solitary Wave Solutions for the Conformable Perturbed Nonlinear Schrodinger Equation With Power Law Nonlinearity(Amer Scientific Publishers, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Gulsen, Selahattin; Baleanu, Dumitru; Inc, MustafaIn this study, we apply three integration schemes to extract optical soliton solutions for the conformable perturbed nonlinear Schrodinger equation (CPNLSE) with power law nonlinearity (PLN). The integration schemes that are used to carry out such solutions are Sine-Cosine (SC), generalized tanh (GT), and Ricatti-Bernoulli (RB) sub-ODE methods. The constraints conditions for the existence of the solutions are reported. The solutions are obtained using newly proposed fractional derivative called conformable derivative. Numerical simulations of some of the obtained solutions are also illustrated.Article Citation - WoS: 27Citation - Scopus: 31Soliton Structures To Some Time-Fractional Nonlinear Differential Equations With Conformable Derivative(Springer, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, MustafaThis research presents new soliton structures to some time-fractional nonlinear differential equations (TFNDEs) with conformable derivative. The powerful Ricatti-Bernoulli (RB) sub-ODE method is used to carry out the soliton solutions. Some of the obtained solutions include trigonometric, periodic wave and hyperbolic solutions. The constraint conditions for the existence of solitons are also presented. The RB sub-ODE method proves to be efficient and effective for the extraction of soliton structures for different types of TFNDEs. Some interesting figures for the numerical simulation of the obtained results are presented.