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  • Küçük Resim Yok
    Öğe
    Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam-Hyers stability and travelling waves
    (Springer Basel Ag, 2024) Bensassa, Kamel; Dahmani, Zoubir; Rakah, Mahdi; Sarıkaya, Mehmet Zeki
    In this paper, we study a coupled system of beam deflection type that involves nonlinear equations with sequential Caputo fractional derivatives. Under flexible/fixed end-conditions, two main theorems on the existence and uniqueness of solutions are proved by using two fixed point theorems. Some examples are discussed to illustrate the applications of the existence and uniqueness of solution results. Another main result on the Ulam-Hyers stability of solutions for the introduced system is also discussed. Some examples of stability are discussed. New travelling wave solutions are obtained for another conformable coupled system of beam type that has a connection with the first considered system. A conclusion follows at the end.
  • 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.