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On a class of langevin equations in the frame of caputo function-dependent-kernel fractional derivatives with antiperiodic boundary conditions

AIMS Mathematics, ISSN: 2473-6988, Vol: 6, Issue: 6, Page: 5518-5534
2021
  • 17
    Citations
  • 0
    Usage
  • 3
    Captures
  • 0
    Mentions
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Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    17
    • Citation Indexes
      17
  • Captures
    3

Article Description

In this manuscript, we consider a class of nonlinear Langevin equations involving two different fractional orders in the frame of Caputo fractional derivative with respect to another monotonic function ϑ with antiperiodic boundary conditions. The existence and uniqueness results are proved for the suggested problem. Our approach is relying on properties of ϑ-Caputo’s derivative, and implementation of Krasnoselskii’s and Banach’s fixed point theorem. At last, we discuss the Ulam-Hyers stability criteria for a nonlinear fractional Langevin equation. Some examples justifying the results gained are provided. The results are novel and provide extensions to some of the findings known in the literature.

Bibliographic Details

Abdelatif Boutiara; Mohammed S. Abdo; Manar A. Alqudah; Thabet Abdeljawad

American Institute of Mathematical Sciences (AIMS)

Mathematics

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