Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Abbas, MuhammadScopus Q: search.filters.scopusQuartile.Q2

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 20
    Citation - Scopus: 23
    Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation
    (Tech Science Press, 2021) Abbas, Muhammad; Baleanu, Dumitru; Iqbal, Muhammad Kashif; Riaz, Muhammad Bilal; Amin, Muhammad
    This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.
  • Article
    Citation - WoS: 34
    Citation - Scopus: 35
    A Numerical Approach of a Time Fractional Reaction-Diffusion Model With a Non-Singular Kernel
    (Mdpi, 2020) Abbas, Muhammad; Ali, Ajmal; Iqbal, Azhar; Baleanu, Dumitru; Akram, Tayyaba
    The time-fractional reaction-diffusion (TFRD) model has broad physical perspectives and theoretical interpretation, and its numerical techniques are of significant conceptual and applied importance. A numerical technique is constructed for the solution of the TFRD model with the non-singular kernel. The Caputo-Fabrizio operator is applied for the discretization of time levels while the extended cubic B-spline (ECBS) function is applied for the space direction. The ECBS function preserves geometrical invariability, convex hull and symmetry property. Unconditional stability and convergence analysis are also proved. The projected numerical method is tested on two numerical examples. The theoretical and numerical results demonstrate that the order of convergence of 2 in time and space directions.
  • Article
    Citation - WoS: 32
    Citation - Scopus: 39
    A Novel 2-Stage Fractional Runge-Kutta Method for a Time-Fractional Logistic Growth Model
    (Hindawi Ltd, 2020) Baleanu, Dumitru; Riaz, Muhammad Bilal; Abbas, Muhammad; Arshad, Muhammad Sarmad
    In this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge-Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge-Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method.
  • Article
    Citation - WoS: 36
    Citation - Scopus: 37
    Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation
    (Mdpi, 2020) Abbas, Muhammad; Iqbal, Azhar; Baleanu, Dumitru; Asad, Jihad H.; Akram, Tayyaba
    The telegraph model describes that the current and voltage waves can be reflected on a wire, that symmetrical wave patterns can form along a line. A numerical study of these voltage and current waves on a transferral line has been proposed via a modified extended cubic B-spline (MECBS) method. The B-spline functions have the flexibility and high order accuracy to approximate the solutions. These functions also preserve the symmetrical property. The MECBS and Crank Nicolson technique are employed to find out the solution of the non-linear time fractional telegraph equation. The time direction is discretized in the Caputo sense while the space dimension is discretized by the modified extended cubic B-spline. The non-linearity in the equation is linearized by Taylor's series. The proposed algorithm is unconditionally stable and convergent. The numerical examples are displayed to verify the authenticity and implementation of the method.