Existence results for Langevin equations involving generalized Liouville–Caputo fractional derivatives with non-local boundary conditions

Sombir Dhaniya, Anoop Kumar*, Aziz Khan, Thabet Abdeljawad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The main objective of the present paper is to establish the existence and uniqueness (EU) results for nonlinear fractional Langevin equation involving Liouville-Caputo generalized fractional derivative (GFD) of different order with non-local boundary conditions. The existence solution is obtained by using Krasnoselskii's fixed point theorem, and the uniqueness result is obtained by using the Banach contraction mapping principle. An example is introduced to validate the effectiveness of the results. The results are novel and provide an extension to some of the findings known in the literature.

Original languageEnglish
Pages (from-to)153-160
Number of pages8
JournalAlexandria Engineering Journal
Volume90
DOIs
Publication statusPublished - Mar 2024
Externally publishedYes

Keywords

  • Banach contraction mapping principle
  • Generalized fractional operator
  • Krasonoselskii's fixed point theorem
  • Langevin equation (LE)
  • Liouville–Caputo generalized fractional derivative (GFD)
  • Non-local boundary conditions

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