Yazar "Gouari, Yazid" seçeneğine göre listele

Listeleniyor 1 - 3 / 3
  • Küçük Resim Yok
    Öğe
    A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling waves
    (Vilnius Gediminas Tech Univ, 2025) Lamamri, Abdelkader; Gouari, Yazid; Dahmani, Zoubir; Rakah, Mahdi; Sarikaya, Mehmet Zeki
    In this work, we begin by introducing a new notion of coupled closed fractional boundary conditions to study a class of nonlinear sequential systems of Caputo fractional differential equations. The existence and uniqueness of solutions for the class of systems is proved by applying Banach contraction principle. The existence of at least one solution is then accomplished by applying Schauder fixed point theorem. The Ulam Hyers stability, with a limiting-case example, is also discussed. In a second part of our work, we use the tanh method to obtain a new travelling wave solution for the coupled system of Burgers using time and space Khalil derivatives. By bridging these two aspects, we aim to present an understanding of the system's behaviour.
  • Küçük Resim
    Öğe
    A nonlocal multi-point singular fractional integro-differential problem of Lane-Emden type
    (Wiley, 2020) Gouari, Yazid; Dahmani, Zoubir; Sarıkaya, Mehmet Zeki
    In this paper, using Riemann-Liouville integral and Caputo derivative, we study a nonlinear singular integro-differential equation of Lane-Emden type with nonlocal multi-point integral conditions. We prove the existence and uniqueness of solutions by application of Banach contraction principle. Also, we prove an existence result using Schaefer fixed point theorem. Then, we present some examples to show the applicability of the main results.
  • Küçük Resim Yok
    Öğe
    Uniqueness of solutions, stability and simulations for a differential problem involving convergent series and time variable singularities
    (Rocky Mt Math Consortium, 2023) Gouari, Yazid; Dahmani, Zoubir; Belhamiti, Meriem Mansouria; Sarıkaya, Mehmet Zeki
    We study a new problem of nonlinear integrodifferential equations with nonlocal integral conditions. The considered problem is singular at the origin of the time axis and it involves convergent series combined with Riemann-Liouville integrals. We prove an existence and uniqueness result for our problem. Some examples are given to illustrate the uniqueness result. The Ulam-Hyers stability for the problem is also studied. Then, thanks to some numerical techniques, that allow us to approximate the Caputo derivatives, and by using the Runge-Kutta method, we present a numerical study with some simulations to show more comprehension of the proposed examples.