Scopus İndeksli Yayınlar Koleksiyonu

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

Browse

Filters

2017 - 201922020 - 20223

Settings

Has files: NoSubject: search.filters.subject.Caputo'S Fractional Derivative

Search Results

Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 6
    Citation - Scopus: 9
    Neutral Functional Sequential Differential Equations With Caputo Fractional Derivative on Time Scales
    (Springernature, 2022) Lazreg, Jamal Eddine; Benkhettou, Nadia; Benchohra, Mouffak; Karapinar, Erdal
    In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray-Schauder type and Krasnoselskii fixed point theorem. As applications, two examples are included to show the applicability of our results.
  • Article
    Citation - WoS: 58
    Citation - Scopus: 61
    Solving Time Fractional Burgers' and Fisher's Equations Using Cubic B-Spline Approximation Method
    (Springer, 2020) Kamran, Mohsin; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Majeed, Abdul
    This article presents a numerical algorithm for solving time fractional Burgers' and Fisher's equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank-Nicolson scheme based on cubic B-spline functions is used to interpolate the solution curve along the spatial grid. The numerical scheme has been implemented on three test problems. The obtained results indicate that the proposed method is a good option for solving nonlinear fractional Burgers' and Fisher's equations. The error norms L2 and L infinity have been calculated to validate the efficiency and accuracy of the presented algorithm.
  • 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.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 37
    Extended Cubic B-Splines in the Numerical Solution of Time Fractional Telegraph Equation
    (Springer, 2019) Abbas, Muhammad; Ismail, Ahmad Izani; Ali, Norhashidah Hj M.; Baleanu, Dumitru; Akram, Tayyaba
    A finite difference scheme based on extended cubic B-spline method for the solution of time fractional telegraph equation is presented and discussed. The Caputo fractional formula is used in the discretization of the time fractional derivative. A combination of the Caputo fractional derivative together with an extended cubic B-spline is utilized to obtain the computed solutions. The proposed scheme is shown to possess the unconditional stability property with second order convergence. Numerical results demonstrate the applicability, simplicity and the strength of the scheme in solving the time fractional telegraph equation with accuracies very close to the exact solutions.
  • Article
    Citation - WoS: 56
    Citation - Scopus: 66
    Existence Theorems and Hyers-Ulam Stability for a Coupled System of Fractional Differential Equations With P-Laplacian Operator
    (Springer, 2017) Li, Yongjin; Chen, Wen; Baleanu, Dumitru; Khan, Aziz; Khan, Hasib
    In this paper, we study the existence and uniqueness of solution (EUS) as well as Hyers-Ulam stability for a coupled system of FDEs in Caputo's sense with nonlinear p-Laplacian operator. For this purpose, the suggested coupled system is transferred to an integral system with the help of four Green functions G(alpha 1) (t, s), G(beta 1) (t, s), G(alpha 2) (t, s), G(beta 2) (t, s). Then using topological degree theory and Leray-Schauder's-type fixed point theorem, existence and uniqueness results are proved. An illustrative and expressive example is given as an application of the results.