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COAR Access Rights: search.filters.coarAccessRights.open accessSubject: search.filters.subject.Conformable Derivative

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  • Article
    Citation - Scopus: 25
    On the Geometric and Physical Properties of Conformable Derivative
    (Murat TOSUN, 2024) Has, A.; Yılmaz, B.; Baleanu, D.
    In this article, we explore the advantages geometric and physical implications of the conformable derivative. One of the key benefits of the conformable derivative is its ability to approximate the tangent at points where the classical tangent is not readily available. By employing conformable derivatives, alternative tangents can be created to overcome this limitation. Thanks to these alternative (conformable) tangents, physical interpretation can be made with alternative velocity vectors. Furthermore, the conformable derivative proves to be valuable in situations where the tangent plane cannot be defined. It enables the creation of alternative tangent planes, offering a solution in cases where the traditional approach falls short. Geometrically speaking, the conformable derivative carries significant meaning. It provides insights into the local behavior of a function and its relationship with nearby points. By understanding the conformable derivative, we gain a deeper understanding of how a function evolves and changes within its domain. A several examples are presented in the article to better understand the article and visualize the concepts discussed. These examples are accompanied by visual representations generated using the Mathematica program, aiding in a clearer understanding of the proposed ideas. By combining theoretical explanations, practical examples, and visualizations, this article aims to provide a comprehensive exploration of the advantages and geometric and physical implications of the conformable derivative. © MSAEN.
  • Article
    Citation - WoS: 35
    Citation - Scopus: 34
    New Optical Solitons of Conformable Resonant Nonlinear Schrodinger's Equation
    (de Gruyter Poland Sp Z O O, 2020) Rezazadeh, Hadi; Abazari, Reza; Khater, Mostafa M. A.; Inc, Mustafa; Baleanu, Dumitru
    Sardar subequation approach, which is one of the strong methods for solving nonlinear evolution equations, is applied to conformable resonant Schrodinger's equation. In this technique, if we choose the special values of parameters, then we can acquire the travelling wave solutions. We conclude that these solutions are the solutions obtained by the first integral method, the trial equation method, and the functional variable method. Several new traveling wave solutions are obtained including generalized hyperbolic and trigonometric functions. The new derivation is of conformable derivation introduced by Atangana recently. Solutions are illustrated with some figures.
  • Article
    Citation - Scopus: 14
    The Effect of Deformation of Special Relativity by Conformable Derivative
    (Sociedad Mexicana de Fisica, 2022) Al-Masaeed, M.; Rabei, E.M.; Baleanu, D.; Al-Jamel, A.
    In this paper, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory are re-stated. Then, the addition of velocity laws are derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, the conformable Klein-Gordon equation, and conformable Dirac equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium. © 2022, Revista Mexicana de Fisica. All Rights Reserved.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 13
    Exact Solutions of Stochastic Kdv Equation With Conformable Derivatives in White Noise Environment
    (Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Ulutas, Esma
    In this article, we have considered Wick-type stochastic Korteweg de Vries (KdV) equation with conformable derivatives. By the help of white noise analysis, Hermit transform and extended G/G-expansion method, we have obtained exact travelling wave solutions of KdV equation with conformable derivatives. We have applied the inverse Hermit transform for stochastic soliton solutions and then we have shown how stochastic solutions can be presented as Brownian motion functional solutions by an application example.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 13
    Quantization of Fractional Harmonic Oscillator Using Creation and Annihilation Operators
    (de Gruyter Poland Sp Z O O, 2021) Rabei, Eqab M.; Al-Jamel, Ahmed; Baleanu, Dumitru; Al-Masaeed, Mohamed
    In this article, the Hamiltonian for the conform-able harmonic oscillator used in the previous study [Chung WS, Zare S, Hassanabadi H, Maghsoodi E. The effect of fractional calculus on the formation of quantum-mechan-ical operators. Math Method Appl Sci. 2020;43(11):6950-67.] is written in terms of fractional operators that we called alpha-creation and alpha-annihilation operators. It is found that these operators have the following influence on the energy states. For a given order alpha, the alpha-creation operator pro-motes the state while the alpha-annihilation operator demotes the state. The system is then quantized using these crea-tion and annihilation operators and the energy eigenvalues and eigenfunctions are obtained. The eigenfunctions are expressed in terms of the conformable Hermite func-tions. The results for the traditional quantum harmonic oscillator are found to be recovered by setting alpha = 1.
  • Article
    Citation - Scopus: 4
    Nonlinear singular p-Laplacian boundary value problems in the frame of conformable derivative
    (American Institute of Mathematical Sciences, 2021) Bouloudene, Mokhtar; Alqudah, Manar A.; Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet
    This paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions. © 2021 American Institute of Mathematical Sciences. All rights reserved.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Nonlinear Singular P-Laplacian Boundary Value Problems in the Frame of Conformable Derivative
    (Amer inst Mathematical Sciences-aims, 2021) Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; Bouloudene, Mokhtar; Alqudah, Manar A.
    This paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions.
  • Article
    Citation - Scopus: 6
    Computational Solutions of Conformable Space-Time Derivatives Dynamical Wave Equations: Analytical Mathematical Techniques
    (Elsevier B.V., 2020) Seadawy, A.R.; Baleanu, D.; Ali, A.
    In this article, the instigator sets up the profuse traveling wave solutions four types of fractional nonlinear equations in the sense of conformable derivatives by using the novel form of modified mathematical technique. The constructed traveling wave solutions are articulated in terms of trigonometric, hyperbolic and exponential functions. The derived results are fruitful for the physical demonstrations of problems in mathematical physics and engineering. © 2020 The Authors
  • Article
    Citation - WoS: 24
    Citation - Scopus: 26
    Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique
    (Mdpi, 2020) Alimgeer, Khurram Saleem; Nawaz, Sidra; Waheed, Asif; Suleman, Muhammad; Baleanu, Dumitru; Atif, M.; Javeed, Shumaila
    This paper is based on finding the exact solutions for Burger's equation, Zakharov-Kuznetsov (ZK) equation and Kortewegde vries (KdV) equation by utilizing exponential function method that depends on the series of exponential functions. The exponential function method utilizes the homogeneous balancing principle to find the solutions of nonlinear equations. This method is simple, wide-reaching and helpful for finding the exact solution of nonlinear conformable PDEs.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 23
    First Integral Technique for Finding Exact Solutions of Higher Dimensional Mathematical Physics Models
    (Mdpi, 2019) Riaz, Sidra; Alimgeer, Khurram Saleem; Atif, M.; Hanif, Atif; Baleanu, Dumitru; Javeed, Shumaila
    In this work, we establish the exact solutions of some mathematical physics models. The first integral method (FIM) is extended to find the explicit exact solutions of high-dimensional nonlinear partial differential equations (PDEs). The considered models are: the space-time modified regularized long wave (mRLW) equation, the (1+2) dimensional space-time potential Kadomtsev Petviashvili (pKP) equation and the (1+2) dimensional space-time coupled dispersive long wave (DLW) system. FIM is a powerful mathematical tool that can be used to obtain the exact solutions of many non-linear PDEs.