International Journal of Nonlinear Analysis and Applications

On a generalized Caputo for Langevin fractional differential equations in Banach spaces

Document Type : Research Paper

Author

Laboratory of Mathematics And Applied Sciences, University of Ghardaia, 47000 Ghardaia. Algeria

Abstract

In this research article, we study the existence, uniqueness and Ulam-Hyers stability of solutions in connection to the generalized Caputo Langevin fractional differential equations in Banach Space. The existence, uniqueness, and stability in the sense of Ulam are established for the proposed system. Our approach is based on the technique of measure of noncompactness combined with the Monch fixed point theorem, the implementation Banach contraction principle fixed point theorem.  Moreover,  the Ulam--Hyers stability is discussed by utilizing the Urs's. Lastly, we deliver an example to check the efficiency and accuracy of the proposed methods.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 12
December 2023
Pages 1-12
  • Receive Date: 22 December 2022
  • Revise Date: 14 August 2023
  • Accept Date: 18 August 2023