Abstract
In this paper, we consider the nonhomogeneous fractional delay oscillation equation with order σ and introduce a class of control functions, i.e., Wright functions. Next, we apply the Cădariu‐Radu method to prove the existence of a unique solution and Hyers‐Ulam‐Rassias‐Wright stability of the fractional delay oscillation equation. At the end of the article, by an example, we show the application of the obtained results.
Highlights
From the past until now, fractional calculus has gained considerable popularity and importance due to its many applications in various and wide scientific and engineering fields
Since the control function used in this article is a Wright function, we start this section with a definition of the Wright function
We provide a definition of Hyers-UlamRassais-Wright stability; for more details and result, we refer to [15,16,17,18]
Summary
From the past until now, fractional calculus has gained considerable popularity and importance due to its many applications in various and wide scientific and engineering fields (see [1, 2]). Where (1) g: B × Rn ⟶ Rn is an integrable function, m(ρ) ∈ Rn, θ ∈ Rn×n, and ψ ∈ C2([− μ, 0], Rn) denotes constant matrix; μ > 0 is a fixed time and B Nμ for a fixed N ∈ {1, 2, . Let Jσ0 denote the Riemann–Liouville fractional integral operator of order σ ∈ (1, 2). Exact solutions for the differential equation using the exponential function for σ 1 and the matrix sine and matrix cosine for σ 2 are obtained in [3, 4]. In 2018, Li and Wang obtained the exact solution of equation (1) for 0 < σ < 1 using the Mittag–Leffler type matrix function [5,6,7]. By an example, we show the application of the obtained results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
