Some New Properties of the Mittag-Leffler Functions and Their Applications to Solvability and Stability of a Class of Fractional Langevin Differential Equations

• Hamid Baghani ^[1] ; Juan J. Nieto ^[2]
  1. [1] Hakim Sabzevari University

     Hakim Sabzevari University

     Irán

     
  2. [2] Universidade de Santiago de Compostela

     Universidade de Santiago de Compostela

     Santiago de Compostela, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
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• Resumen

  • The paper examines the solvability and stability of a particular set of fractional Langevin equations under anti-periodic boundary conditions. Utilizing the Krasnoselskii fixed point theorem, the Banach contraction mapping theorem, and properties of the Mittag-Leffler function, we establish less stringent criteria for the existence and uniqueness of solutions compared to previous findings in the literature. Furthermore, we present illustrative examples with specific parameters that highlight the reduced conditions necessary for ensuring the existence of a unique solution.