WoS İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Singh, JagdevSubject: search.filters.subject.Caputo Fractional Derivative

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 32
    Citation - Scopus: 38
    On the Analysis of an Analytical Approach for Fractional Caudrey-Dodd Equations
    (Elsevier, 2022) Gupta, Arpita; Baleanu, Dumitru; Singh, Jagdev
    The principal aim of this paper is to study the approximate solution of nonlinear Caudrey-Dodd-Gibbon equation of fractional order by employing an analytical method. The Caudrey-Dodd-Gibbon equation arises in plasma physics and laser optics. The Caputo derivative is applied to model the physical problem. By applying an effective semi-analytical technique, we attain the approximate solutions without linearization. The uniqueness and the convergence analysis for the applied method are shown. The graphical representation of solutions of fractional Caudrey-Dodd-Gibbon equation demonstrates the applied technique is very efficient to obtain the solutions of such type of fractional order mathematical models. (c) 2021 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
    Citation - WoS: 53
    Citation - Scopus: 58
    An Efficient Computational Technique for Fractional Model of Generalized Hirota-Satsuma Korteweg-De Vries and Coupled Modified Korteweg-De Vries Equations
    (Asme, 2020) Prakasha, D. G.; Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Veeresha, P.
    The aim of the present investigation to find the solution for fractional generalized Hirota-Satsuma coupled Korteweg-de-Vries (KdV) and coupled modified KdV (mKdV) equations with the aid of an efficient computational scheme, namely, fractional natural decomposition method (FNDM). The considered fractional models play an important role in studying the propagation of shallow-water waves. Two distinct initial conditions are choosing for each equation to validate and demonstrate the effectiveness of the suggested technique. The simulation in terms of numeric has been demonstrated to assure the proficiency and reliability of the future method. Further, the nature of the solution is captured for different value of the fractional order. The comparison study has been performed to verify the accuracy of the future algorithm. The achieved results illuminate that, the suggested computational method is very effective to investigate the considered fractional-order model.
  • Article
    Citation - WoS: 143
    Citation - Scopus: 159
    An Efficient Numerical Algorithm for the Fractional Drinfeld-Sokolov Equation
    (Elsevier Science inc, 2018) Kumar, Devendra; Baleanu, Dumitru; Rathore, Sushila; Singh, Jagdev
    The fundamental purpose of the present paper is to apply an effective numerical algorithm based on the mixture of homotopy analysis technique, Sumudu transform approach and homotopy polynomials to obtain the approximate solution of a nonlinear fractional Drinfeld-Sokolov-Wilson equation. The nonlinear Drinfeld-Sokolov-Wilson equation naturally occurs in dispersive water waves. The uniqueness and convergence analysis are shown for the suggested technique. The convergence of the solution is fixed and managed by auxiliary parameter h. The numerical results are shown graphically. Results obtained by the application of the technique disclose that the suggested scheme is very accurate, flexible, effective and simple to use. (C) 2018 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 44
    Citation - Scopus: 49
    A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships
    (Mdpi, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, Jagdev
    In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian's decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter h and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.