Well-Posedness of a Class of Fractional Langevin Equations

• Mi Zhou ^[1] ; Lu Zhang ^[2]
  1. [1] University of South China

     University of South China

     China

     
  2. [2] Xiangtan University

     Xiangtan University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this work, we deal with a more general form of fractional Langevin equation.

    The equation’s nonlinearity term f is relevant to fractional integral and fractional derivative. By using the fixed point theorems, we study the existence and uniqueness of solutions of initial value problem for the nonlinear fractional Langevin equation and obtain some new results. Further, by using the technique of nonlinear functional analysis, we study the stability of Ulam-Hyers, Ulam-Hyers-Rassias and semi-UlamHyers-Rassias for the initial value problem of nonlinear Langevin equation. Finally, some examples are given to show the effectiveness of theoretical results.