Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Jarad, FahdSubject: search.filters.subject.Laplace Transform

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Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 52
    Citation - Scopus: 54
    Fractional Caputo Heat Equation Within the Double Laplace Transform
    (Editura Acad Romane, 2013) Jarad, Fahd; Anwar, A. M. O.; Jarad, Fahd; Baleanu, Dumitru; Baleanu, D.; Ayaz, F.; Matematik
    The heat equation and its fractional generalization are used in various applications in science and engineering. In this paper firstly we introduce the double Laplace transform of the partial fractional integrals and derivatives which can be used to solve partial differential equations with Caputo fractional derivatives. Secondly, the fractional heat equation was investigated in details with the help of this new generalized transform
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    On the Quantitative Weighted Generalization of Jafari Transform
    (Univ Nis, Fac Sci Math, 2025) Yazici, Serdal; Cekim, Bayram; Jarad, Fahd; Jafari, Hossein
    In this paper, a quantitative weighted transform based on the Jafari transform is proposed, and the mathematical foundations of this new transform are investigated. In the first section, some information about Jafari transform and some mathematical tools are reviewed. In the second section, the quantitative weighted Jafari transform is introduced, its existence guaranteed through a theorem, and its fundamental properties are examined. Additionally, transforms of the fractional derivative and fractional integral of a function with respect to a function h and a w-weight are obtained. In the third section, the theoretical findings are applied to solve classical and fractional initial value problems based on a function h and w-weight. In the last section, the results are discussed.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Heat Transfer of Mhd Oldroyd-B Fluid With Ramped Wall Velocity and Temperature in View of Local and Nonlocal Differential Operators
    (World Scientific Publ Co Pte Ltd, 2022) Riaz, Muhammad Bilal; Jarad, Fahd; Asgir, Maryam; Zafar, Azhar Ali
    The theoretical study focuses on the examination of the convective flow of Oldroyd-B fluid with ramped wall velocity and temperature. The fluid is confined on an extended, unbounded vertical plate saturated within the permeable medium. To depict the fluid flow, the coupled partial differential equations are settled by using the Caputo (C) and Caputo Fabrizio (CF) differential time derivatives. The mathematical analysis of the fractionalized models of fluid flow is performed by Laplace transform (LT). The complexity of temperature and velocity profile is explored by numerical inversion algorithms of Stehfest and Tzou. The fractionalized solutions of the temperature and velocity profile have been traced out under fractional and other different parameters considered. The physical impacts of associated parameters are elucidated with the assistance of the graph using the software MATHCAD 15. We noticed the significant influence of the fractional parameter (memory effects) and other parameters on the dynamics of the fluid flow. Shear stress at the wall and Nusselt number also are considered. It's brought into notice the fractional-order model (CF) is the best fit in describing the memory effects in comparison to the C model. An analysis of the comparison between the solution of velocity and temperature profile for ramped wall temperature and velocity and constant wall temperature and velocity is also performed.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 8
    Analytic and Numerical Solutions of Discrete Bagley-Torvik Equation
    (Springer, 2021) Khashan, M. Motawi; Xavier, Gnanaprakasam Britto Antony; Jarad, Fahd; Meganathan, Murugesan; Abdeljawad, Thabet; Britto Antony Xavier, Gnanaprakasam; Motawi Khashan, M.
    In this research article, a discrete version of the fractional Bagley-Torvik equation is proposed: del(2)(h)u(t) + A(C)del(nu)(h) u(t) + Bu(t) = f (t), t > 0, (1) where 0 < nu < 1 or 1 < nu < 2, subject to u(0) = a and del(h)u(0) = b, with a and b being real numbers. The solutions are obtained by employing the nabla discrete Laplace transform. These solutions are expressed in terms of Mittag-Leffler functions with three parameters. These solutions are handled numerically for some examples with specific values of some parameters.
  • Article
    Citation - Scopus: 1
    Alpha Fractional Frequency Laplace Transform Through Multiseries
    (Springer, 2020) Gnanaprakasam, Britto Antony Xavier; Jarad, Fahd; Murugesan, Meganathan; Abdeljawad, Thabet
    Our main goal in this work is to derive the frequency Laplace transforms of the products of two and three functions with tuning factors. We propose the Laplace transform for certain types of multiseries of circular functions as well. For use in numerical results, we derive a finite summation formula and m-series formulas. Moreover, we discuss various explanatory examples.