WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Author: search.filters.author.Hashemi, Mir SajjadScopus Q: search.filters.scopusQuartile.Q1

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  • Article
    Citation - WoS: 7
    Citation - Scopus: 6
    New Solutions of Nonlinear Dispersive Equation in Higher-Dimensional Space With Three Types of Local Derivatives
    (Mdpi, 2022) Hashemi, Mir Sajjad; Jarad, Fahd; Akgul, Ali
    The aim of this paper is to use the Nucci's reduction method to obtain some novel exact solutions to the s-dimensional generalized nonlinear dispersive mK(m,n) equation. To the best of the authors' knowledge, this paper is the first work on the study of differential equations with local derivatives using the reduction technique. This higher-dimensional equation is considered with three types of local derivatives in the temporal sense. Different types of exact solutions in five cases are reported. Furthermore, with the help of the Maple package, the solutions found in this study are verified. Finally, several interesting 3D, 2D and density plots are demonstrated to visualize the nonlinear wave structures more efficiently.
  • Article
    Citation - WoS: 45
    Citation - Scopus: 50
    A Reduction Technique To Solve the Generalized Nonlinear Dispersive Mk(M,n) Equation With New Local Derivative
    (Elsevier, 2022) Jarad, Fahd; Hashemi, Mir Sajjad; Riaz, Muhammad Bilal; Xia, Fang-Li
    In this work, we consider the generalized nonlinear dispersive mK(m,n) equation with a recently defined local derivative in the temporal direction. Different types of exact solutions are extracted by Nucci's reduction technique. Combinations of the exponential, trigonometric, hyperbolic, and logarithmic functions constitute the exact solutions especially of the soliton and Kink-type soliton solutions. The influence of the derivative order alpha, for the obtained results, is graphically investigated. In some cases, exact solutions are achieved for arbitrary values of n and m, which can be interesting from the mathematical point of view. We provided 2-D and 3-D figures to illustrate the reported solutions. Computational results indicate that the reduction technique is superior to some other methods used in the literature to solve the same equations. To the best of the author's knowledge, this method is not applied for differential equations with the recently hyperbolic local derivative.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 4
    A New Application of the Legendre Reproducing Kernel Method
    (Amer inst Mathematical Sciences-aims, 2022) Hashemi, Mir Sajjad; Gholizadeh, Leila; Akgul, Ali; Jarad, Fahd; Foroutan, Mohammad Reza
    In this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.