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    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.
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    SOLVABILITY FOR A COUPLED SYSTEM OF 4-SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS
    (Element, 2024) Bensassa, Kamel; Dahmani, Zoubir; Sarikaya, Mehmet zeki
    The present work deals with a coupled system of fractional differential equations involving four sequential Caputo derivatives in each of its components. The fractional differential system gives rise to a standard coupled system of two ordinary differential equations of order four, which has practical applications in some real-world phenomena such as robotics, aerospace, and electrical engineering. The existence of a unique vector solution for our sequential system is studied. The existence of at least one vector solution for the considered system is also investigated. Some illustrative examples are discussed in detail to show the main results' applicability. The stabilities in the sense of Ulam Hyers for the system is discussed. A conclusion follows at the end.