Scopus İndeksli Yayınlar Koleksiyonu

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

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Publisher: search.filters.publisher.SpringeropenSubject: search.filters.subject.Fractional Differential Equations

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Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 14
    Citation - Scopus: 16
    The Invariant Subspace Method for Solving Nonlinear Fractional Partial Differential Equations With Generalized Fractional Derivatives
    (Springeropen, 2020) Kader, Abass H. Abdel; Baleanu, Dumitru; Latif, Mohamed S. Abdel; Abdel Latif, Mohamed S.; Abdel Kader, Abass H.
    In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the time fractional Hunter-Saxton equation, a time fractional nonlinear diffusion equation, a time fractional thin-film equation, the fractional Whitman-Broer-Kaup-type equation, and a system of time fractional diffusion equations.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 15
    Computation of Iterative Solutions Along With Stability Analysis To a Coupled System of Fractional Order Differential Equations
    (Springeropen, 2019) Abdeljawad, Thabet; Shah, Kamal; Jarad, Fahd; Arif, Muhammad; Ali, Sajjad
    In this research article, we investigate sufficient results for the existence, uniqueness and stability analysis of iterative solutions to a coupled system of the nonlinear fractional differential equations (FDEs) with highier order boundary conditions. The foundation of these sufficient techniques is a combination of the scheme of lower and upper solutions together with the method of monotone iterative technique. With the help of the proposed procedure, the convergence criteria for extremal solutions are smoothly achieved. Furthermore, a major aspect is devoted to the investigation of Ulam-Hyers type stability analysis which is also established. For the verification of our work, we provide some suitable examples along with their graphical represntation and errors estimates.
  • Article
    Citation - WoS: 140
    Citation - Scopus: 161
    A New Fractional Model for Giving Up Smoking Dynamics
    (Springeropen, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, Jagdev; Qurashi, Maysaa Al
    The key purpose of the present work is to examine a fractional giving up smoking model pertaining to a new fractional derivative with non-singular kernel. The numerical simulations are conducted with the aid of an iterative technique. The existence of the solution is discussed by employing the fixed point postulate, and the uniqueness of the solution is also proved. The effect of various parameters is shown graphically. The numerical results for the smoking model associated with the new fractional derivative are compared with numerical results for a smoking model pertaining to the standard derivative and Caputo fractional derivative.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 9
    Approximate Solution of Linear and Nonlinear Fractional Differential Equations Under M-Point Local and Nonlocal Boundary Conditions
    (Springeropen, 2016) Khan, Rahmat Ali; Baleanu, Dumitru; Saker, Samir H.; Khalil, Hammad
    This paper investigates a computational method to find an approximation to the solution of fractional differential equations subject to local and nonlocal m-point boundary conditions. The method that we will employ is a variant of the spectral method which is based on the normalized Bernstein polynomials and its operational matrices. Operational matrices that we will developed in this paper have the ability to convert fractional differential equations together with its nonlocal boundary conditions to a system of easily solvable algebraic equations. Some test problems are presented to illustrate the efficiency, accuracy, and applicability of the proposed method.
  • Article
    Citation - WoS: 102
    Citation - Scopus: 114
    Laplace Homotopy Analysis Method for Solving Linear Partial Differential Equations Using a Fractional Derivative With and Without Kernel Singular
    (Springeropen, 2016) Francisco Gomez-Aguilar, Jose; Yepez-Martinez, Huitzilin; Baleanu, Dumitru; Fabricio Escobar-Jimenez, Ricardo; Hugo Olivares-Peregrino, Victor; Fabian Morales-Delgado, Victor; Olivares-Peregrino, Victor Hugo; Morales-Delgado, Victor Fabian; Gómez-Aguilar, José Francisco; Escobar-Jimenez, Ricardo Fabricio
    In this work, we present an analysis based on a combination of the Laplace transform and homotopy methods in order to provide a new analytical approximated solutions of the fractional partial differential equations (FPDEs) in the Liouville-Caputo and Caputo-Fabrizio sense. So, a general scheme to find the approximated solutions of the FPDE is formulated. The effectiveness of this method is demonstrated by comparing exact solutions of the fractional equations proposed with the solutions here obtained.