Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Jarad, FahdSubject: search.filters.subject.Fractional Differential Equations

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Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    Qualitative Analysis of a Fuzzy Volterra-Fredholm Integrodifferential Equation With an Atangana-Baleanu Fractional Derivative
    (Amer inst Mathematical Sciences-aims, 2022) Shah, Kamal; Jarad, Fahd; Abdo, Mohammed S.; Abdeljawad, Thabet; Almalahi, Mohammed A.; Panchal, Satish K.
    The point of this work was to analyze and investigate the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fuzzy fractional Volterra Fredholm integrodifferential equation in the frame of the Atangana-Baleanu-Caputo fractional derivative methodology. To begin with, we give the parametric interval form of the Atangana-Baleanu-Caputo fractional derivative on fuzzy set-valued functions. Then, by employing Schauder???s and Banach???s fixed point procedures, we examine the existence and uniqueness of solutions for fuzzy fractional Volterra Fredholm integro-differential equation with the Atangana-Baleanu-Caputo fractional operator. It turns out that the last interval model is a combined arrangement of nonlinear equations. In addition, we consider results by applying the Adams Bashforth fractional technique and present two examples that have been numerically solved using graphs.
  • Article
    Citation - WoS: 68
    Citation - Scopus: 81
    Efficient Sustainable Algorithm for Numerical Solutions of Systems of Fractional Order Differential Equations by Haar Wavelet Collocation Method
    (Elsevier, 2020) Shah, Kamal; Al-Mdallal, Qasem; Jarad, Fahd; Abdeljawad, Thabet; Amin, Rohul
    This manuscript deals a numerical technique based on Haar wavelet collocation which is developed for the approximate solution of some systems of linear and nonlinear fractional order differential equations (FODEs). Based on these techniques, we find the numerical solution to var-ious systems of FODEs. We compare the obtain solution with the exact solution of the considered problems at integer orders. Also, we compute the maximum absolute error to demonstrate the effi-ciency and accuracy of the proposed method. For the illustration of our results we provide four test examples. The experimental rates of convergence for different number of collocation point is calculated which is approximately equal to 2. Fractional derivative is defined in the Caputo sense. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
  • 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: 11
    Citation - Scopus: 12
    On Stable Iterative Solutions for a Class of Boundary Value Problem of Nonlinear Fractional Order Differential Equations
    (Wiley, 2019) Shah, Kamal; Jarad, Fahd; Ali, Sajjad
    In this article, sufficient conditions for the existence of extremal solutions to nonlinear boundary value problem (BVP) of fractional order differential equations (FDEs) are provided. By using the method of monotone iterative technique together with upper and lower solutions, conditions for the existence and approximation of minimal and maximal solutions to the BVP under consideration are constructed. Some adequate results for different kinds of Ulam stability are investigated. Maximum error estimates for the corresponding solutions are given as well. Two examples are provided to illustrate the results.
  • Article
    Citation - WoS: 109
    Citation - Scopus: 113
    Applying New Fixed Point Theorems on Fractional and Ordinary Differential Equations
    (Springer, 2019) Karapinar, Erdal; Abdeljawad, Thabet; Jarad, Fahd
    In this paper, we consider a fixed point theorem that extends and unifies several existing results in the literature. We apply the proven fixed point results on the existence of solution of ordinary boundary value problems and fractional boundary value problems with integral type boundary conditions in the frame of some Caputo type fractional operators.