Existence and Ulam-Hyers stability results for nonlinear fractional Langevin equation with modified argument


DEVELİ F.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1002/mma.7987
  • Title of Journal : MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Keywords: Caputo fractional derivative, existence and uniqueness, fixed point, Langevin equation, Ulam-Hyers stability, INTEGRAL-EQUATIONS, UNIQUENESS, ORDERS

Abstract

In this paper, we give the existence and uniqueness result for the fractional order Langevin equation with modified argument by using the Bielecki norm. After, we consider a special form of this equation (delayed form) and then apply Burton's method to this special form to prove that there is a unique solution under weaker conditions than the other result. Further, we derive the Ulam-Hyers stability for this equation. Finally, two examples are given to illustrate our main results.