Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Now showing 1 - 10 of 61
  • Article
    Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,Qx
    (Wiley, 2026) Guldogan Lekesiz, Esra
    Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szeg & odblac;-Hermite polynomials, in the literature. In this paper, we derive for the first time a pair of finite univariate biorthogonal polynomials suggested by the finite univariate orthogonal polynomials . The corresponding biorthogonality relation and some useful relations and properties, including differential equation and generating function, are presented. Further, a new family of finite biorthogonal functions is obtained using Fourier transform and Parseval identity. In addition, we compute the Laplace transform and fractional calculus operators for the new biorthogonal polynomial set .
  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    On Modeling the Groundwater Flow Within a Confined Aquifer
    (Editura Acad Romane, 2015) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
    The groundwater flow equation is used to simulate the movement of water under the confined aquifer. In this paper we study a modification of the groundwater flow equation within a newly proposed derivative. We numerically solve the generalized groundwater flow equation with the Crank-Nicholson scheme. We also analytically solve the generalized equation via the method of separation of variable.
  • Article
    Citation - WoS: 69
    Citation - Scopus: 73
    Classical and Fractional Aspects of Two Coupled Pendulums
    (Editura Acad Romane, 2019) Baleanu, D.; Baleanu, Dumitru; Jajarmi, A.; Asad, J. H.; Matematik
    In this study, we consider two coupled pendulums (attached together with a spring) having the same length while the same masses are attached at their ends. After setting the system in motion we construct the classical Lagrangian, and as a result, we obtain the classical Euler-Lagrange equation. Then, we generalize the classical Lagrangian in order to derive the fractional Euler-Lagrange equation in the sense of two different fractional operators. Finally, we provide the numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on the Euler method to discretize the convolution integral. Numerical simulations show that the proposed approach is efficient and demonstrate new aspects of the real-world phenomena.
  • Article
    Citation - WoS: 67
    Citation - Scopus: 69
    The Fractional Model of Spring Pendulum: New Features Within Different Kernels
    (Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; Matematik
    In this work, new aspects of the fractional calculus (FC) are examined for a model of spring pendulum in fractional sense. First, we obtain the classical Lagrangian of the model, and as a result, we derive the classical Euler-Lagrange equations of the motion. Second, we generalize the classical Lagrangian to fractional case and derive the fractional Euler-Lagrange equations in terms of fractional derivatives with singular and nonsingular kernels, respectively. Finally, we provide the numerical solution of these equations within two fractional operators for some fractional orders and initial conditions. Numerical simulations verify that taking into account the recently features of the FC provides more realistic models demonstrating hidden aspects of the real-world phenomena.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 7
    About Fractional Calculus of Singular Lagrangians
    (Fuji Technology Press Ltd, 2005) Baleanu, Dumitru
    In this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. We observed that if a Lagrangian is singular in the classical sense, it remains singular after being fractionally generalized. The fractional Lagrangian is non-local but its gauge symmetry was preserved despite complexity of equations in fractional cases. We generalized four examples of singular Lagrangians admitting gauge symmetry in fractional case and found solutions to corresponding Euler-Lagrange equations.
  • Book Part
    Citation - WoS: 25
    Citation - Scopus: 1
    New Treatise in Fractional Dynamics
    (Springer-verlag Berlin, 2012) Baleanu, Dumitru; Baleanu, Dumitru
    Fractional calculus becomes a powerful tool used to investigate complex phenomena from various fields of science and engineering. In this context, the researchers paid a lot of attention for the fractional dynamics. However, the fractional modeling is still at the beginning of its developing. The aim of this chapter is to present some new results in the area of fractional dynamics and its applications.
  • Article
    Citation - WoS: 98
    Citation - Scopus: 112
    Analysis and Some Applications of a Regularized Ψ-Hilfer Fractional Derivative
    (Elsevier, 2022) Jajarmi, Amin; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Nieto, Juan J.
    The main purpose of this research is to present a generalization of Psi-Hilfer fractional derivative, called as regularized Psi-Hilfer, and study some of its basic characteristics. In this direction, we show that the psi-Riemann-Liouville integral is the inverse operation of the presented regularized differentiation by means of the same function psi. In addition, we consider an initial-value problem comprising this generalization and analyze the existence as well as the uniqueness of its solution. To do so, we first present an approximation sequence via a successive substitution approach; then we prove that this sequence converges uniformly to the unique solution of the regularized Psi-Hilfer fractional differential equation (FDE). To solve this FDE, we suggest an efficient numerical scheme and show its accuracy and efficacy via some real-world applications. Simulation results verify the theoretical consequences and show that the regularized Psi-Hilfer fractional mathematical system provides a more accurate model than the other kinds of integer- and fractional-order differential equations. (C) 2022 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 30
    Citation - Scopus: 33
    Dynamics of Fractional Order Delay Model of Coronavirus Disease
    (Amer inst Mathematical Sciences-aims, 2022) Zhang, Lei; Rahman, Mati Ur; Ahmad, Shabir; Riaz, Muhammad Bilal; Jarad, Fahd
    The majority of infectious illnesses, such as HIV/AIDS, Hepatitis, and coronavirus (2019-nCov), are extremely dangerous. Due to the trial version of the vaccine and different forms of 2019-nCov like beta, gamma, delta throughout the world, still, there is no control on the transmission of coronavirus. Delay factors such as social distance, quarantine, immigration limitations, holiday extensions, hospitalizations, and isolation are being utilized as essential strategies to manage the outbreak of 2019-nCov. The effect of time delay on coronavirus disease transmission is explored using a non-linear fractional order in the Caputo sense in this paper. The existence theory of the model is investigated to ensure that it has at least one and unique solution. The Ulam-Hyres (UH) stability of the considered model is demonstrated to illustrate that the stated model's solution is stable. To determine the approximate solution of the suggested model, an efficient and reliable numerical approach (Adams-Bashforth) is utilized. Simulations are used to visualize the numerical data in order to understand the behavior of the different classes of the investigated model. The effects of time delay on dynamics of coronavirus transmission are shown through numerical simulations via MATLAB-17.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 4
    Numerical Analysis of Fractional Order Discrete Bloch Equa-Tions
    (int Scientific Research Publications, 2024) Santra, Shyam Sundar; Jayanathan, Leo Amalraj; Baleanu, Dumitru; Murugesan, Meganathan
    By defining a new kind of h-extorial function with constant coefficient, this research seeks to solve discrete fractional Bloch equations. By using an extorial function of the Mittag-Leffler type, we are able to discover the general solutions for the magnetization's Bx, By, and Bz components. These findings demonstrate the innovative method of fractional order Bloch equations. In addition, we offer a graphical representation of our results.(c) 2024 All rights reserved.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 23
    Optical Solitons With Nonlinear Dispersion in Parabolic Law Medium and Three-Component Coupled Nonlinear Schrodinger Equation
    (Springer, 2022) Sulaiman, Tukur Abdulkadir; Alshomrani, Ali S.; Baleanu, Dumitru; Yusuf, Abdullahi
    The current study looks at two different nonlinear Schrodinger equations. These equations have several applications in science and engineering, such as nonlinear fiber optics, electromagnetic field waves, and signal processing via optical fibers. In this study, we investigate these equations using an efficient integration strategy known as complex envelop antazs. As a result, we obtain novel solutions such as bright, dark, and combined dark-bright soliton solutions. Important physical aspects have been depicted in three dimensions and contour plots for clear interpretation of the acquired solutions.