English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The main aim of this paper is to prove the Ulam–Hyers stability of solutions for a new form of nonlinear fractional Langevin differential equations involving two fractional orders in the  ψ -Caputo sense. Prior to proceeding to the main results, the proposed system is converted into an equivalent integral form by the help of fractional calculus. Next, we proceed to investigate the existence and uniqueness of the solution by applying Schauder and Banach fixed point theorems. Finally, we study the Ulam–Hyers stability criteria for the main fractional system. Illustrative examples are presented to demonstrate the validity of the obtained results. The results are new and provide extensions to some known results in the literature.

Ulam stability for nonlinear-Langevin fractional differential equations involving two fractional orders in the ψ -Caputo sense