Browsing by Author "Supervisor: KHIRANI, Amina"

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    Modified Homotopy Perturbation Method For Solving Fractional Differential Equations
    (UNIVERSITY of M'SILA, 2022) BENCHOUIKH, Cheyma; Supervisor: KHIRANI, Amina
    In this work, we applied two modifications of He’s homotopy perturbation method HPM suggested by Momani and Odibat to obtaining solutions of linear (nonlinear) ordinary (partial) differential equations of fractional order. The fractional derivative is described in the Caputo sense. Some illustrative examples are given to reveal the effectiveness and convenience of these modifications.
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    Spline Collocation For Fredholm Integral Equations
    (University of m'sila, 2022-06-10) BAKOUR, Safa; Supervisor: KHIRANI, Amina
    In this thesis we study the integral equations, whose the general form is u (x) = f (x) + R (x) (x) k (x; t) u (t) dt where (x) and (x) the limits of integration and u(x) unknown function; K(x; t)the kernel and f(x) function in equation, and is a constant parameter. particularly, we study the Fredholm Integral equation, we 1. Outline these equation using basic deÖnitions. 2. Discuss the existence and uniqueness of solutions. 3. Approximate the solution of Fredholm integral equation, using spline colloction method compared to colloction basis on Lagrange method.