Scopus İndeksli Yayınlar Koleksiyonu

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

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Now showing 1 - 10 of 24
  • 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: 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.
  • 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: 132
    Citation - Scopus: 158
    On a New and Generalized Fractional Model for a Real Cholera Outbreak
    (Elsevier, 2022) Ghassabzade, Fahimeh Akhavan; Nieto, Juan J.; Jajarmi, Amin; Baleanu, Dumitru
    In this paper, a new mathematical model involving the general form of Caputo fractional derivative is studied for a real case of cholera outbreak. Fundamental properties of the new model including the equilibrium points as well as the basic reproduction number are explored. Also, an efficient approximation scheme on the basis of product-integration rule is established to solve the new model. Several kernel functions for the general fractional derivative are tested, and the results are compared with the real data of a cholera outbreak in Yemen. As a consequence, we find a special case in which the aforesaid outbreak is described better, for the corresponding numerical simulations are closer to the real data than the other classical and fractional frameworks. Next, we apply the most realistic model to investigate the effect of vaccination on the considered cholera outbreak. Simulation results show that earlier vaccination could reduce the number of infected individuals effectively, so mortality would have been reduced considerably if the vaccination had been performed earlier. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
  • Article
    On Hilbert-Pachpatte Type Inequalities Within ?-Hilfer Fractional Generalized Derivatives
    (Amer inst Mathematical Sciences-aims, 2023) Baleanu, Dumitru; Basci, Yasemin
    In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided psi-Hilfer fractional derivatives with the general kernel. Our results are a generalization of the inequalities of Pecaric ' and Vukovic ' [1]. Furthermore, using the specific cases of the psi-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting psi, a1, b1 and considering the limit of the parameters alpha and beta.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 20
    Comprehending the Model of Omicron Variant Using Fractional Derivatives
    (Taylor & Francis Ltd, 2023) Goswami, Pranay; Baleanu, Dumitru; Shankar Dubey, Ravi; Sharma, Shivani
    The world is grappled with an unprecedented challenges due to Corona virus. We are all battling this epidemic together, but we have not been able to defeat this epidemic yet. A new variant of this virus, named 'Omicron' is spreading these days. The fractional differential equations are providing us with better tools to study the mathematical model with memory effects. In this paper, we will consider an extended SER mathematical model with quarantined and vaccinated compartment to speculate the Omicron variant. This extended Susceptible Exposed Infected Recovered SER model involves equations that associate with the group of individuals those are susceptible (S), exposed (E): this class includes the individuals who are infected but not yet infectious, infectious (W): this class includes the individuals who are infected but not yet Quarantined, quarantined (Q): this class includes those group of people who are infectious, confirmed and quarantined, recovered (R) this class includes the group of individuals who have recovered, and vaccinated (V): this class includes the group of individuals who have been vaccinated. The non-negativity and of the extended SER model is analysed, the equilibrium points and the basic reproduction number are also calculated. The proposed model is then extended to the mathematical model using AB derivative operator. Proof for the existence and the uniqueness for the solution of fractional mathematical model in sense of AB fractional derivative is detailed and a numerical method is detailed to obtain the numerical solutions. Further we have discussed the efficiency of the vaccine against the Omicron variant via graphical representation.
  • Article
    Citation - WoS: 35
    Citation - Scopus: 31
    Optimal Solutions for Singular Linear Systems of Caputo Fractional Differential Equations
    (Wiley, 2021) Baleanu, Dumitru; Dassios, Ioannis
    In this article, we focus on a class of singular linear systems of fractional differential equations with given nonconsistent initial conditions (IC). Because the nonconsistency of the IC can not lead to a unique solution for the singular system, we use two optimization techniques to provide an optimal solution for the system. We use two optimization techniques to provide the optimal solution for the system because a unique solution for the singular system cannot be obtained due to the non-consistency of the IC. These two optimization techniques involve perturbations to the non-consistent IC, specifically, an l(2) perturbation (which seeks an optimal solution for the system in terms of least squares), and a second-order optimization technique at an l(1) minimum perturbation, (which includes an appropriate smoothing). Numerical examples are given to justify our theory. We use the Caputo (C) fractional derivative and two recently defined alternative versions of this derivative, the Caputo-Fabrizio (CF) and the Atangana-Baleanu (AB) fractional derivative.
  • Article
    Citation - WoS: 91
    Citation - Scopus: 98
    Novel Hyperbolic and Exponential Ansatz Methods To the Fractional Fifth-Order Korteweg-De Vries Equations
    (Springer, 2020) Nuruddeen, R., I; Ali, Khalid K.; Muhammad, Lawal; Osman, M. S.; Baleanu, Dumitru; Park, Choonkil
    This paper aims to investigate the class of fifth-order Korteweg-de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.
  • Article
    Citation - WoS: 24
    Citation - Scopus: 34
    Coupled Transform Method for Time-Space Fractional Black-Scholes Option Pricing Model
    (Elsevier, 2020) Jena, R. M.; Chakraverty, S.; Baleanu, D.; Edeki, S. O.
    This paper presents analytical solutions of a time-space-fractional Black-Scholes model (TSFBSM) using a coupled technique referred to as Fractional Complex Transform (FCT) with the aid of a modified differential transform method. The nature of the derivatives is in the sense of Jumarie. The considered cases and applications show more consistency of the TSFBSM with an actual integer and fractional data when compared with the classical Black-Scholes model. The method is noted to be very effective, even with little knowledge of fractional calculus. Extension of this to multi-factor models formulated in terms of stochastic dynamics is highly recommended. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.