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

  1. Hamid Baghani 1
  2. Juan J. Nieto 2
  1. 1 Hakim Sabzevari University
    info

    Hakim Sabzevari University

    Sabzevar, Irán

    ROR https://ror.org/00zyh6d22

  2. 2 Universidade de Santiago de Compostela
    info

    Universidade de Santiago de Compostela

    Santiago de Compostela, España

    ROR https://ror.org/030eybx10

Journal:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Year of publication: 2024

Volume: 23

Issue: 1

Type: Article

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Abstract

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.

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